Robinson-Trautman solutions to Einstein's equations

NASA Astrophysics Data System (ADS)

Davidson, William

2017-02-01

Solutions to Einstein's equations in the form of a Robinson-Trautman metric are presented. In particular, we derive a pure radiation solution which is non-stationary and involves a mass m, The resulting spacetime is of Petrov Type II A special selection of parametric values throws up the feature of the particle `rocket', a Type D metric. A suitable transformation of the complex coordinates allows the metrics to be expressed in real form. A modification, by setting m to zero, of the Type II metric thereby converting it to Type III, is then shown to admit a null Einstein-Maxwell electromagnetic field.

Stability of stationary-axisymmetric black holes in vacuum general relativity to axisymmetric electromagnetic perturbations

NASA Astrophysics Data System (ADS)

Prabhu, Kartik; Wald, Robert M.

2018-01-01

We consider arbitrary stationary and axisymmetric black holes in general relativity in (d +1) dimensions (with d ≥slant 3 ) that satisfy the vacuum Einstein equation and have a non-degenerate horizon. We prove that the canonical energy of axisymmetric electromagnetic perturbations is positive definite. This establishes that all vacuum black holes are stable to axisymmetric electromagnetic perturbations. Our results also hold for asymptotically de Sitter black holes that satisfy the vacuum Einstein equation with a positive cosmological constant. Our results also apply to extremal black holes provided that the initial perturbation vanishes in a neighborhood of the horizon.

Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dotti, Gustavo; Instituto de Fisica Enrique Gaviola, CONICET, Cordoba; Oliva, Julio

2010-07-15

The classification of a certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is performed in d{>=}5 dimensions. The class of metrics under consideration is such that the spacelike section is a warped product of the real line and an arbitrary base manifold. It is shown that for a generic value of the Gauss-Bonnet coupling, the base manifold must be necessarily Einstein, with an additional restriction on its Weyl tensor for d>5. The boundary admits a wider class of geometries only in the special case when the Gauss-Bonnet coupling is such that the theory admits a unique maximallymore » symmetric solution. The additional freedom in the boundary metric enlarges the class of allowed geometries in the bulk, which are classified within three main branches, containing new black holes and wormholes in vacuum.« less

Taming the nonlinearity of the Einstein equation.

PubMed

Harte, Abraham I

2014-12-31

Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate all such nonlinearities beyond a particular order: Both Landau-Lifshitz and tetrad formulations of Einstein's equation are obtained that involve only finite products of the unknowns and their derivatives. Considerable additional simplifications arise in physically interesting cases where metrics become approximately Kerr or, e.g., plane waves, suggesting that the variables described here can be used to efficiently reformulate perturbation theory in a variety of contexts. In all cases, these variables are shown to have simple geometrical interpretations that directly relate the local causal structure associated with the metric of interest to the causal structure associated with a prescribed background. A new method to search for exact solutions is outlined as well.

Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

NASA Astrophysics Data System (ADS)

Ayissi, Raoul Domingo; Noutchegueme, Norbert

2015-01-01

Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the

Through the big bang: Continuing Einstein's equations beyond a cosmological singularity

NASA Astrophysics Data System (ADS)

Koslowski, Tim A.; Mercati, Flavio; Sloan, David

2018-03-01

All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them is changed. Here we develop a description for classical Bianchi IX cosmology implementing these relational principles. The objective evolution decouples from the volume and its expansion degree of freedom. We use the relational description to investigate both vacuum dominated and quiescent Bianchi IX cosmologies. In the vacuum dominated case the relational dynamical system predicts an infinite amount of change of the relational DOFs, in accordance with the well known chaotic behaviour of Bianchi IX. In the quiescent case the relational dynamical system evolves uniquely though the point where the decoupled scale DOFs predict the big bang/crunch. This is a non-trivial prediction of the relational description; the big bang/crunch is not the end of physics - it is instead a regular point of the relational evolution. Describing our solutions as spacetimes that satisfy Einstein's equations, we find that the relational dynamical system predicts two singular solutions of GR that are connected at the hypersurface of the singularity such that relational DOFs are continuous and the orientation of the spatial frame is inverted.

Casimir effect in the rainbow Einstein's universe

NASA Astrophysics Data System (ADS)

Bezerra, V. B.; Mota, H. F.; Muniz, C. R.

2017-10-01

In the present paper we investigate the effects caused by the modification of the dispersion relation obtained by solving the Klein-Gordon equation in the closed Einstein's universe in the context of rainbow's gravity models. Thus, we analyse how the quantum vacuum fluctuations of the scalar field are modified when compared with the results obtained in the usual General Relativity scenario. The regularization, and consequently the renormalization, of the vacuum energy is performed adopting the Epstein-Hurwitz and Riemann's zeta functions.

Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ayissi, Raoul Domingo, E-mail: raoulayissi@yahoo.fr; Noutchegueme, Norbert, E-mail: nnoutch@yahoo.fr

Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academymore » of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol

New exact perfect fluid solutions of Einstein's equations. II

NASA Astrophysics Data System (ADS)

Uggla, Claes; Rosquist, Kjell

1990-12-01

A family of new spatially homogeneous Bianchi type VIh perfect fluid solutions of the Einstein equations is presented. The fluid flow is orthogonal to the spatially homogeneous hypersurfaces, and the pressure is proportional to the energy density.

The Einstein equations on the 3-brane world

NASA Astrophysics Data System (ADS)

Shiromizu, Tetsuya; Maeda, Kei-Ichi; Sasaki, Misao

2000-07-01

We carefully investigate the gravitational equations of the brane world, in which all the matter forces except gravity are confined on the 3-brane in a 5-dimensional spacetime with Z2 symmetry. We derive the effective gravitational equations on the brane, which reduce to the conventional Einstein equations in the low energy limit. From our general argument we conclude that the first Randall-Sundrum-type theory predicts that the brane with a negative tension is an antigravity world and hence should be excluded from the physical point of view. Their second-type theory where the brane has a positive tension provides the correct signature of gravity. In this latter case, if the bulk spacetime is exactly anti-de Sitter spacetime, generically the matter on the brane is required to be spatially homogeneous because of the Bianchi identities. By allowing deviations from anti-de Sitter spacetime in the bulk, the situation will be relaxed and the Bianchi identities give just the relation between the Weyl tensor and the energy momentum tensor. In the present brane world scenario, the effective Einstein equations cease to be valid during an era when the cosmological constant on the brane is not well defined, such as in the case of the matter dominated by the potential energy of the scalar field.

Simplified derivation of the gravitational wave stress tensor from the linearized Einstein field equations.

PubMed

Balbus, Steven A

2016-10-18

A conserved stress energy tensor for weak field gravitational waves propagating in vacuum is derived directly from the linearized general relativistic wave equation alone, for an arbitrary gauge. In any harmonic gauge, the form of the tensor leads directly to the classical expression for the outgoing wave energy. The method described here, however, is a much simpler, shorter, and more physically motivated approach than is the customary procedure, which involves a lengthy and cumbersome second-order (in wave-amplitude) calculation starting with the Einstein tensor. Our method has the added advantage of exhibiting the direct coupling between the outgoing wave energy flux and the work done by the gravitational field on the sources. For nonharmonic gauges, the directly derived wave stress tensor has an apparent index asymmetry. This coordinate artifact may be straightforwardly removed, and the symmetrized (still gauge-invariant) tensor then takes on its widely used form. Angular momentum conservation follows immediately. For any harmonic gauge, however, the stress tensor found is manifestly symmetric from the start, and its derivation depends, in its entirety, on the structure of the linearized wave equation.

An exact solution to the Einstein-Maxwell equations representing a nonspherical, highly charged object

NASA Astrophysics Data System (ADS)

Menon, Govind K.

The Reissner-Nordstrom solution possesses a naked singularity when e2 > m2, where m is the mass and e is the net charge of the system. Also, the singularity at r = 0 is repulsive (i.e., no timelike geodesics (neutral particles) can reach the singularity). These unusual properties of the Reissner-Nordstrom geometry are considered as an accident resulting from the highly symmetric nature of the space-time. Here we wish to generalize the condition of spherical symmetry to axial symmetry and to probe into the issues of naked singularity and gravitational repulsion. To do this, we must construct a nonspherical solution to the Einstein-Maxwell set of equations in the event that e2 > m2. The Erez-Rosen extension of the vacuum Schwarzschild solution to the non-spherical case gave one of the first physically significant solutions of the Einstein field equations. Nonvacuum extensions of the Erez-Rosen solution representing a non-spherical mass containing a very high net charge (i.e., when e2 > m2) will be discussed. The special case of spherical symmetry, as would be expected, results in the Reissner-Nordstrom solution. The search for the physical singularities involves the calculation of a nontrivial scalar constructed from the Riemann curvature tensor. As it turns out, the resulting geometry does indeed possess a naked singularity. In addition, the space-time also entertains gravitational repulsion. However, unlike the Reissner-Nordstrom solution, it has been found that all timelike geodesics are not necessarily repelled from the origin.

Einstein Equations Under Polarized U (1) Symmetry in an Elliptic Gauge

NASA Astrophysics Data System (ADS)

Huneau, Cécile; Luk, Jonathan

2018-06-01

We prove local existence of solutions to the Einstein-null dust system under polarized U (1) symmetry in an elliptic gauge. Using in particular the previous work of the first author on the constraint equations, we show that one can identify freely prescribable data, solve the constraints equations, and construct a unique local in time solution in an elliptic gauge. Our main motivation for this work, in addition to merely constructing solutions in an elliptic gauge, is to provide a setup for our companion paper in which we study high frequency backreaction for the Einstein equations. In that work, the elliptic gauge we consider here plays a crucial role to handle high frequency terms in the equations. The main technical difficulty in the present paper, in view of the application in our companion paper, is that we need to build a framework consistent with the solution being high frequency, and therefore having large higher order norms. This difficulty is handled by exploiting a reductive structure in the system of equations.

Nonlinear Schrödinger equations for Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Galati, Luigi; Zheng, Shijun

2013-10-01

The Gross-Pitaevskii equation, or more generally the nonlinear Schrödinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the NLS with L2 initial data in order to understand propagation of the defocusing and focusing waves for the BEC mechanism in the presence of electromagnetic fields. Numerical simulations are performed for the two-dimensional GPE with anisotropic quadratic potentials.

A Generalization of the Einstein-Maxwell Equations

NASA Astrophysics Data System (ADS)

Cotton, Fredrick

2016-03-01

The proposed modifications of the Einstein-Maxwell equations include: (1) the addition of a scalar term to the electromagnetic side of the equation rather than to the gravitational side, (2) the introduction of a 4-dimensional, nonlinear electromagnetic constitutive tensor and (3) the addition of curvature terms arising from the non-metric components of a general symmetric connection. The scalar term is defined by the condition that a spherically symmetric particle be force-free and mathematically well-behaved everywhere. The constitutive tensor introduces two auxiliary fields which describe the particle structure. The additional curvature terms couple both to particle solutions and to electromagnetic and gravitational wave solutions. http://sites.google.com/site/fwcotton/em-30.pdf

Cosmological Constant: A Lesson from Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Finazzi, Stefano; Liberati, Stefano; Sindoni, Lorenzo

2012-02-01

The cosmological constant is one of the most pressing problems in modern physics. We address this issue from an emergent gravity standpoint, by using an analogue gravity model. Indeed, the dynamics of the emergent metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. The direct computation of this term shows that in emergent gravity scenarios this constant may be naturally much smaller than the naive ground-state energy of the emergent effective field theory. This suggests that a proper computation of the cosmological constant would require a detailed understanding about how Einstein equations emerge from the full microscopic quantum theory. In this light, the cosmological constant appears as a decisive test bench for any quantum or emergent gravity scenario.

Cosmological constant: a lesson from Bose-Einstein condensates.

PubMed

Finazzi, Stefano; Liberati, Stefano; Sindoni, Lorenzo

2012-02-17

The cosmological constant is one of the most pressing problems in modern physics. We address this issue from an emergent gravity standpoint, by using an analogue gravity model. Indeed, the dynamics of the emergent metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. The direct computation of this term shows that in emergent gravity scenarios this constant may be naturally much smaller than the naive ground-state energy of the emergent effective field theory. This suggests that a proper computation of the cosmological constant would require a detailed understanding about how Einstein equations emerge from the full microscopic quantum theory. In this light, the cosmological constant appears as a decisive test bench for any quantum or emergent gravity scenario.

Particle creation phenomenology, Dirac sea and the induced Weyl and Einstein-dilaton gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N., E-mail: berezin@inr.ac.ru, E-mail: dokuchaev@inr.ac.ru, E-mail: eroshenko@inr.ac.ru

We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the 'usual' hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by 'the particle creation law', proportional to the square of the Weyl tensor (following the famous result by Ya.B. Zel'dovich and A.A. Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein-Hilbert gravity action integral with dilaton field. Thus, we obtained something like the induced gravity suggested firstmore » by A.D. Sakharov. It is shown that the resulting system is self-consistent. We considered also the vacuum equations. It is shown that, beside the 'empty vacuum', there may exist the 'dynamical vacuum', which is nothing more but the Dirac sea. The latter is described by the unexpectedly elegant equation which includes both the Bach and Einstein tensors and the cosmological terms.« less

Shear free, twisting Einstein-Maxwell metrics in the Newman-Penrose formalism

NASA Technical Reports Server (NTRS)

Lind, R. W.

1972-01-01

The problem of finding algebraically special solutions to the vacuum Einstein-Maxwell equations was investigated using a spin coefficient formalism. The general case in which the degenerate null vectors are not hypersurface orthogonal is reduced to a problem of solving five coupled differential equations that are no longer dependent on the affine parameter along the degenerate null directions. It is shown that the most general regular, shear-free, nonradiating solution to these equations is the Kerr-Newman metric.

Einstein-Cartan Theory of Gravitation: Kinematical Parameters and Maxwell Equations

NASA Astrophysics Data System (ADS)

Katkar, L. N.

2015-03-01

In the space-time manifold of Einstein-Cartan Theory (ECT) of gravitation, the expressions for the time-like kinematical parameters are derived and the propagation equation for expansion is obtained.It has been observed that when the spin tensor is u-orthogonal the spin of the gravitating matter has no influence on the propagation equation of expansion while it has influence when it is not u-orthogonal. The usual formula for the curl of gradient of a scalar function is not zero in ECT. So is the case with the divergence of the curl of a vector.Their expressions on the space-time manifold of ECT are derived. A new derivative operator d ∗ is introduced to develop the calculus on space-time manifold of ECT. It is obtained by taking the covariant derivative of an associated tensor of a form with respect to an asymmetric connections. We have used this differential operator to obtain the form of the Maxwell's equations in the ECT of gravitation. Cartan's equations of structure are also derived through the new derivative operator. It has been shown that unlike the consequences of exterior derivative in Einstein space-time, the repetition of d ∗ on a form of any degree is not zero.

Averaging problem in general relativity, macroscopic gravity and using Einstein's equations in cosmology.

NASA Astrophysics Data System (ADS)

Zalaletdinov, R. M.

1998-04-01

The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the geometry of macroscopic space-time, which follows from averaging Cartan's structure equations, is described and the correlation tensors present in the theory are discussed. The macroscopic field equations (averaged Einstein's equations) derived in the framework of the approach are presented and their structure is analysed. The correspondence principle for macroscopic gravity is formulated and a definition of the stress-energy tensor for the macroscopic gravitational field is proposed. It is shown that the physical meaning of using Einstein's equations with a hydrodynamic stress-energy tensor in looking for cosmological models means neglecting all gravitational field correlations. The system of macroscopic gravity equations to be solved when the correlations are taken into consideration is given and described.

Posing Einstein's Question: Questioning Einstein's Pose.

ERIC Educational Resources Information Center

Topper, David; Vincent, Dwight E.

2000-01-01

Discusses the events surrounding a famous picture of Albert Einstein in which he poses near a blackboard containing a tensor form of his 10 field equations for pure gravity with a question mark after it. Speculates as to the content of Einstein's lecture and the questions he might have had about the equation. (Contains over 30 references.) (WRM)

On static solutions of the Einstein-Scalar Field equations

NASA Astrophysics Data System (ADS)

Reiris, Martín

2017-03-01

In this article we study self-gravitating static solutions of the Einstein-Scalar Field system in arbitrary dimensions. We discuss the existence of geodesically complete solutions depending on the form of the scalar field potential V(φ ), and provide full global geometric estimates when the solutions exist. The most complete results are obtained for the physically important Klein-Gordon field and are summarised as follows. When V(φ )=m2|φ |2, it is proved that geodesically complete solutions have Ricci-flat spatial metric, have constant lapse and are vacuum, (that is φ is constant and equal to zero if m≠ 0). In particular, when the spatial dimension is three, the only such solutions are either Minkowski or a quotient thereof (no nontrivial solutions exist). When V(φ )=m2|φ |2+2Λ , that is, when a vacuum energy or a cosmological constant is included, it is proved that no geodesically complete solution exists when Λ >0, whereas when Λ <0 it is proved that no non-vacuum geodesically complete solution exists unless m2<-2Λ /(n-1), ( n is the spatial dimension) and the spatial manifold is non-compact. The proofs are based on novel techniques in comparison geometry á la Bakry-Émery that have their own interest.

On the existence of the field line solutions of the Einstein-Maxwell equations

NASA Astrophysics Data System (ADS)

Vancea, Ion V.

The main result of this paper is the proof that there are local electric and magnetic field configurations expressed in terms of field lines on an arbitrary hyperbolic manifold. This electromagnetic field is described by (dual) solutions of the Maxwell’s equations of the Einstein-Maxwell theory. These solutions have the following important properties: (i) they are general, in the sense that the knot solutions are particular cases of them and (ii) they reduce to the electromagnetic fields in the field line representation in the flat space-time. Also, we discuss briefly the real representation of these electromagnetic configurations and write down the corresponding Einstein equations.

A numerical approach to finding general stationary vacuum black holes

NASA Astrophysics Data System (ADS)

Adam, Alexander; Kitchen, Sam; Wiseman, Toby

2012-08-01

The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon, this equation has previously been shown to be elliptic, and Ricci flow and Newton’s method provide good numerical algorithms to solve it. Here we extend these techniques to the arbitrary cohomogeneity stationary case which must be treated in Lorentzian signature. For stationary spacetimes with globally timelike Killing vector the Harmonic Einstein equation is elliptic. In the presence of horizons and ergo-regions it is less obviously so. Motivated by the Rigidity theorem we study a class of stationary black hole spacetimes which is general enough to include many interesting higher dimensional solutions. We argue the Harmonic Einstein equation consistently truncates to this class of spacetimes giving an elliptic problem. The Killing horizons and axes of rotational symmetry are boundaries for this problem and we determine boundary conditions there. As a simple example we numerically construct 4D rotating black holes in a cavity using Anderson’s boundary conditions. We demonstrate both Newton’s method and Ricci flow to find these Lorentzian solutions.

Einstein's equations and a cosmology with finite matter

NASA Astrophysics Data System (ADS)

Clavelli, L.; Goldstein, Gary R.

2015-05-01

We discuss various space-time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass.1 In this alternative cosmology, the matter density was postulated to be a spatial delta function at the time of the big bang thereafter diffusing outward with constant total mass. This proposal explores a departure from standard assumptions that the big bang occurred everywhere at once or was just one of an infinite number of previous and later transitions.

Well-posedness, linear perturbations, and mass conservation for the axisymmetric Einstein equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dain, Sergio; Ortiz, Omar E.; Facultad de Matematica, Astronomia y Fisica, FaMAF, Universidad Nacional de Cordoba, Instituto de Fisica Enrique Gaviola, IFEG, CONICET, Ciudad Universitaria

2010-02-15

For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides a nonlinear control of the variables along the whole evolution. In this gauge, Einstein equations reduce to a coupled hyperbolic-elliptic system which is formally singular at the axis. As a first step in analyzing this system of equations we study linear perturbations on a flat background. We prove that the linear equations reduce to a very simple system of equations which provide, thoughmore » the mass formula, useful insight into the structure of the full system. However, the singular behavior of the coefficients at the axis makes the study of this linear system difficult from the analytical point of view. In order to understand the behavior of the solutions, we study the numerical evolution of them. We provide strong numerical evidence that the system is well-posed and that its solutions have the expected behavior. Finally, this linear system allows us to formulate a model problem which is physically interesting in itself, since it is connected with the linear stability of black hole solutions in axial symmetry. This model can contribute significantly to solve the nonlinear problem and at the same time it appears to be tractable.« less

Conformal and covariant Z4 formulation of the Einstein equations: Strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes

NASA Astrophysics Data System (ADS)

Dumbser, Michael; Guercilena, Federico; Köppel, Sven; Rezzolla, Luciano; Zanotti, Olindo

2018-04-01

We present a strongly hyperbolic first-order formulation of the Einstein equations based on the conformal and covariant Z4 system (CCZ4) with constraint-violation damping, which we refer to as FO-CCZ4. As CCZ4, this formulation combines the advantages of a conformal and traceless formulation, with the suppression of constraint violations given by the damping terms, but being first order in time and space, it is particularly suited for a discontinuous Galerkin (DG) implementation. The strongly hyperbolic first-order formulation has been obtained by making careful use of first and second-order ordering constraints. A proof of strong hyperbolicity is given for a selected choice of standard gauges via an analytical computation of the entire eigenstructure of the FO-CCZ4 system. The resulting governing partial differential equations system is written in nonconservative form and requires the evolution of 58 unknowns. A key feature of our formulation is that the first-order CCZ4 system decouples into a set of pure ordinary differential equations and a reduced hyperbolic system of partial differential equations that contains only linearly degenerate fields. We implement FO-CCZ4 in a high-order path-conservative arbitrary-high-order-method-using-derivatives (ADER)-DG scheme with adaptive mesh refinement and local time-stepping, supplemented with a third-order ADER-WENO subcell finite-volume limiter in order to deal with singularities arising with black holes. We validate the correctness of the formulation through a series of standard tests in vacuum, performed in one, two and three spatial dimensions, and also present preliminary results on the evolution of binary black-hole systems. To the best of our knowledge, these are the first successful three-dimensional simulations of moving punctures carried out with high-order DG schemes using a first-order formulation of the Einstein equations.

Unimodular Einstein-Cartan gravity: Dynamics and conservation laws

NASA Astrophysics Data System (ADS)

Bonder, Yuri; Corral, Cristóbal

2018-04-01

Unimodular gravity is an interesting approach to address the cosmological constant problem, since the vacuum energy density of quantum fields does not gravitate in this framework, and the cosmological constant appears as an integration constant. These features arise as a consequence of considering a constrained volume element 4-form that breaks the diffeomorphisms invariance down to volume preserving diffeomorphisms. In this work, the first-order formulation of unimodular gravity is presented by considering the spin density of matter fields as a source of spacetime torsion. Even though the most general matter Lagrangian allowed by the symmetries is considered, dynamical restrictions arise on their functional dependence. The field equations are obtained and the conservation laws associated with the symmetries are derived. It is found that, analogous to torsion-free unimodular gravity, the field equation for the vierbein is traceless; nevertheless, torsion is algebraically related to the spin density as in standard Einstein-Cartan theory. The particular example of massless Dirac spinors is studied, and comparisons with standard Einstein-Cartan theory are shown.

Quantum vacuum energy in general relativity

NASA Astrophysics Data System (ADS)

Henke, Christian

2018-02-01

The paper deals with the scale discrepancy between the observed vacuum energy in cosmology and the theoretical quantum vacuum energy (cosmological constant problem). Here, we demonstrate that Einstein's equation and an analogy to particle physics leads to the first physical justification of the so-called fine-tuning problem. This fine-tuning could be automatically satisfied with the variable cosmological term Λ (a)=Λ_0+Λ_1 a^{-(4-ɛ)}, 0 < ɛ ≪ 1, where a is the scale factor. As a side effect of our solution of the cosmological constant problem, the dynamical part of the cosmological term generates an attractive force and solves the missing mass problem of dark matter.

Particle-like solutions of the Einstein-Dirac-Maxwell equations

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

1999-08-01

We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the ground state solutions are discussed for different values of the electromagnetic coupling constant. We find solutions even when the electromagnetic coupling is so strong that the total interaction is repulsive in the Newtonian limit. Our solutions are regular and well-behaved; this shows that the combined electromagnetic and gravitational self-interaction of the Dirac particles is finite.

The Maxwell and Navier-Stokes equations that follow from Einstein equation in a spacetime containing a Killing vector field

NASA Astrophysics Data System (ADS)

Rodrigues, Fabio Grangeiro; Rodrigues, Waldyr Alves, Jr.; da Rocha, Roldão

2012-10-01

In this paper we are concerned to reveal that any spacetime structure , which is a model of a gravitational field in General Relativity generated by an energy-momentum tensor T - and which contains at least one nontrivial Killing vector field A - is such that the 2-form field F = dA (where A = g(A,)) satisfies a Maxwell like equation - with a well determined current that contains a term of the superconducting type- which follows directly from Einstein equation. Moreover, we show that the resulting Maxwell like equations, under an additional condition imposed to the Killing vector field, may be written as a Navier-Stokes like equation as well. As a result, we have a set consisting of Einstein, Maxwell and Navier-Stokes equations, that follows sequentially from the first one under precise mathematical conditions and once some identifications about field variables are evinced, as explained in details throughout the text. We compare and emulate our results with others on the same subject appearing in the literature. In Appendix A we fix our notation and recall some necessary material concerning the theory of differential forms, Lie derivatives and the Clifford bundle formalism used in this paper. Moreover, we comment in Appendix B on some analogies (and main differences) between our results to the ones obtained long ago by Bergmann and Kommar which are reviewed and briefly criticized.

Well-posedness of the Einstein-Euler system in asymptotically flat spacetimes: The constraint equations

NASA Astrophysics Data System (ADS)

Brauer, Uwe; Karp, Lavi

This paper deals with the construction of initial data for the coupled Einstein-Euler system. We consider the condition where the energy density might vanish or tend to zero at infinity, and where the pressure is a fractional power of the energy density. In order to achieve our goals we use a type of weighted Sobolev space of fractional order. The common Lichnerowicz-York scaling method (Choquet-Bruhat and York, 1980 [9]; Cantor, 1979 [7]) for solving the constraint equations cannot be applied here directly. The basic problem is that the matter sources are scaled conformally and the fluid variables have to be recovered from the conformally transformed matter sources. This problem has been addressed, although in a different context, by Dain and Nagy (2002) [11]. We show that if the matter variables are restricted to a certain region, then the Einstein constraint equations have a unique solution in the weighted Sobolev spaces of fractional order. The regularity depends upon the fractional power of the equation of state.

Static black holes with back reaction from vacuum energy

NASA Astrophysics Data System (ADS)

Ho, Pei-Ming; Matsuo, Yoshinori

2018-03-01

We study spherically symmetric static solutions to the semi-classical Einstein equation sourced by the vacuum energy of quantum fields in the curved space-time of the same solution. We found solutions that are small deformations of the Schwarzschild metric for distant observers, but without horizon. Instead of being a robust feature of objects with high densities, the horizon is sensitive to the energy–momentum tensor in the near-horizon region.

Non-CMC solutions to the Einstein constraint equations on asymptotically Euclidean manifolds with apparent horizon boundaries

NASA Astrophysics Data System (ADS)

Holst, Michael; Meier, Caleb

2015-01-01

In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold M with interior boundary Σ. Building on recent results for both the asymptotically Euclidean and compact with boundary settings, we show the existence of far-from-CMC and near-CMC solutions to the conformal formulation of the Einstein constraints when nonlinear Robin boundary conditions are imposed on Σ, similar to those analyzed previously by Dain (2004 Class. Quantum Grav. 21 555-73), by Maxwell (2004, 2005 Commun. Math. Phys. 253 561-83), and by Holst and Tsogtgerel (2013 Class. Quantum Grav. 30 205011) as a model of black holes in various CMC settings, and by Holst et al (2013 Non-CMC solutions to the einstein constraint equations with apparent horizon boundaries arXiv:1310.2302v1) in the setting of far-from-CMC solutions on compact manifolds with boundary. These ‘marginally trapped surface’ Robin conditions ensure that the expansion scalars along null geodesics perpendicular to the boundary region Σ are non-positive, which is considered the correct mathematical model for black holes in the context of the Einstein constraint equations. Assuming a suitable form of weak cosmic censorship, the results presented in this article guarantee the existence of initial data that will evolve into a space-time containing an arbitrary number of black holes. A particularly important feature of our results are the minimal restrictions we place on the mean curvature, giving both near- and far-from-CMC results that are new.

Einstein-Yang-Mills scattering amplitudes from scattering equations

NASA Astrophysics Data System (ADS)

Cachazo, Freddy; He, Song; Yuan, Ellis Ye

2015-01-01

We present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for the scattering of n massless particles are given by integrals over the positions of n points on a sphere restricted to satisfy the scattering equations. As applications, we obtain all single-trace amplitudes in Einstein-Yang-Mills (EYM) theory, and generalizations to include scalars. Also in EYM but extended by a B-field and a dilaton, we present all double-trace gluon amplitudes. The building blocks are made of Pfaffians and Parke-Taylor-like factors of subsets of particle labels.

Vacuum stress energy density and its gravitational implications

NASA Astrophysics Data System (ADS)

Estrada, Ricardo; Fulling, Stephen A.; Kaplan, Lev; Kirsten, Klaus; Liu, Zhonghai; Milton, Kimball A.

2008-04-01

In nongravitational physics the local density of energy is often regarded as merely a bookkeeping device; only total energy has an experimental meaning—and it is only modulo a constant term. But in general relativity the local stress-energy tensor is the source term in Einstein's equation. In closed universes, and those with Kaluza-Klein dimensions, theoretical consistency demands that quantum vacuum energy should exist and have gravitational effects, although there are no boundary materials giving rise to that energy by van der Waals interactions. In the lab there are boundaries, and in general the energy density has a nonintegrable singularity as a boundary is approached (for idealized boundary conditions). As pointed out long ago by Candelas and Deutsch, in this situation there is doubt about the viability of the semiclassical Einstein equation. Our goal is to show that the divergences in the linearized Einstein equation can be renormalized to yield a plausible approximation to the finite theory that presumably exists for realistic boundary conditions. For a scalar field with Dirichlet or Neumann boundary conditions inside a rectangular parallelepiped, we have calculated by the method of images all components of the stress tensor, for all values of the conformal coupling parameter and an exponential ultraviolet cutoff parameter. The qualitative features of contributions from various classes of closed classical paths are noted. Then the Estrada-Kanwal distributional theory of asymptotics, particularly the moment expansion, is used to show that the linearized Einstein equation with the stress-energy near a plane boundary as source converges to a consistent theory when the cutoff is removed. This paper reports work in progress on a project combining researchers in Texas, Louisiana and Oklahoma. It is supported by NSF Grants PHY-0554849 and PHY-0554926.

Raychaudhuri equation in the self-consistent Einstein-Cartan theory with spin-density

NASA Technical Reports Server (NTRS)

Fennelly, A. J.; Krisch, Jean P.; Ray, John R.; Smalley, Larry L.

1988-01-01

The physical implications of the Raychaudhuri equation for a spinning fluid in a Riemann-Cartan spacetime is developed and discussed using the self-consistent Lagrangian based formulation for the Einstein-Cartan theory. It was found that the spin-squared terms contribute to expansion (inflation) at early times and may lead to a bounce in the final collapse. The relationship between the fluid's vorticity and spin angular velocity is clarified and the effect of the interaction terms between the spin angular velocity and the spin in the Raychaudhuri equation investigated. These results should prove useful for studies of systems with an intrinsic spin angular momentum in extreme astrophysical or cosmological problems.

The Spacetime Between Einstein and Kaluza-Klein: Further Explorations

NASA Astrophysics Data System (ADS)

Vuille, Chris

2017-01-01

Tensor multinomials can be used to create a generalization of Einstein's general relativity that in a mathematical sense falls between Einstein's original theory in four dimensions and the Kaluza-Klein theory in five dimensions. In the extended theory there are only four physical dimensions, but the tensor multinomials are expanded operators that can accommodate other forces of nature. The equivalent Ricci tensor of this geometry yields vacuum general relativity and electromagnetism, as well as a Klein-Gordon-like quantum scalar field. With a generalization of the stress-energy tensor, an exact solution for a plane-symmetric dust can be found where the scalar portion of the field drives early universe inflation, levels off for a period, then causes a later continued universal acceleration, a possible geometric mechanism for the inflaton or dark energy. Some new explorations of the equations, the problems, and possibilities will be presented and discussed.

Conformal symmetries of Einstein's field equations and initial data

NASA Astrophysics Data System (ADS)

Sharma, Ramesh

2005-04-01

This paper examines the initial data for the evolution of the space-time solution of Einstein's equations admitting a conformal symmetry. Under certain conditions on the extrinsic curvature of the initial complete spacelike hypersurface and sectional curvature of the space-time with respect to sections containing the normal vector field, we have shown that the initial hypersurface is conformally diffeomorphic to a sphere or a flat space or a hyperbolic space or the product of an open real interval and a complete 2-manifold. It has been further shown that if the initial hypersurface is compact, then it is conformally diffeomorphic to a sphere. Finally, the conformal symmetries of a generalized Robertson-Walker space-time have been described.

Quantum computational complexity, Einstein's equations and accelerated expansion of the Universe

NASA Astrophysics Data System (ADS)

Ge, Xian-Hui; Wang, Bin

2018-02-01

We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume duality in a geodesic causal ball in the framework of Fermi normal coordinates and derive the full non-linear Einstein equation. Using insights from the complexity/action duality, we argue that the accelerated expansion of the universe could be driven by the quantum complexity and free from coincidence and fine-tunning problems.

A family of solutions to the Einstein-Maxwell system of equations describing relativistic charged fluid spheres

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Sharma, Ranjan

2018-05-01

In this paper, we present a formalism to generate a family of interior solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner-Nordström space-time. By reducing the Einstein-Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. A large class of solutions obtained previously are shown to be contained in our general class of solutions. We also analyse the physical viability of our new class of solutions.

The einstein equivalence principle, intrinsic spin and the invariance of constitutive equations in continuum mechanics

NASA Technical Reports Server (NTRS)

Speziale, Charles G.

1988-01-01

The invariance of constitutive equations in continuum mechanics is examined from a basic theoretical standpoint. It is demonstrated the constitutive equations which are not form invariant under arbitrary translational accelerations of the reference frame are in violation of the Einstein equivalane principle. Furthermore, by making use of an analysis based on statistical mechanics, it is argued that any frame-dependent terms in constitutive equations must arise from the intrinsic spin tensor and are negligible provided that the ratio of microscopic to macroscopic time scales is extremely small. The consistency of these results with existing constitutive theories is discussed in detail along with possible avenues of future research.

Quasi-polaritons in Bose-Einstein condensates induced by Casimir-Polder interaction with graphene.

PubMed

Terças, H; Ribeiro, S; Mendonça, J T

2015-06-03

We consider the mechanical coupling between a two-dimensional Bose-Einstein condensate and a graphene sheet via the vacuum fluctuations of the electromagnetic field which are at the origin of the so-called Casimir-Polder potential. By deriving a self-consistent set of equations governing the dynamics of the condensate and the flexural (out-of-plane) modes of the graphene, we can show the formation of a new type of purely acoustic quasi-particle excitation, a quasi-polariton resulting from the coherent superposition of quanta of flexural and Bogoliubov modes.

Classes of exact Einstein Maxwell solutions

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Maharaj, S. D.

2007-12-01

We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

Computation of partially invariant solutions for the Einstein Walker manifolds' identifying equations

NASA Astrophysics Data System (ADS)

Nadjafikhah, Mehdi; Jafari, Mehdi

2013-12-01

In this paper, partially invariant solutions (PISs) method is applied in order to obtain new four-dimensional Einstein Walker manifolds. This method is based on subgroup classification for the symmetry group of partial differential equations (PDEs) and can be regarded as the generalization of the similarity reduction method. For this purpose, those cases of PISs which have the defect structure δ=1 and are resulted from two-dimensional subalgebras are considered in the present paper. Also it is shown that the obtained PISs are distinct from the invariant solutions that obtained by similarity reduction method.

Extensions of the Einstein-Schrodinger non-symmetric theory of gravity

NASA Astrophysics Data System (ADS)

Shifflett, James A.

We modify the Einstein-Schrödinger theory to include a cosmological constant L z which multiplies the symmetric metric. The cosmological constant L z is assumed to be nearly cancelled by Schrödinger's cosmological constant L b which multiplies the nonsymmetric fundamental tensor, such that the total L = L z + L b matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as |L z | [arrow right] oo. For |L z | ~ 1/(Planck length) 2 the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are < 10 -16 of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein- Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. An exact charged solution matches the Reissner-Nordström solution except for additional terms which are ~ 10 -66 of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory. Peri-center advance, deflection of light and time delay of light have a fractional difference of < 10 -56 compared to Einstein-Maxwell theory for worst-case parameters. When a spin-1/2 field is included in the Lagrangian, the theory gives the ordinary Dirac equation, and the charged solution results in fractional shifts of < 10 -50 in Hydrogen atom energy levels. Newman-Penrose methods are used to derive an exact solution of the connection equations, and to show that the charged solution is Petrov

Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rinaldi, Massimiliano, E-mail: massimiliano.rinaldi@unitn.it

We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to mattermore » domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.« less

Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations

NASA Astrophysics Data System (ADS)

Rinaldi, Massimiliano

2015-10-01

We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to matter domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.

Gluon transport equation with effective mass and dynamical onset of Bose–Einstein condensation

DOE PAGES

Blaizot, Jean-Paul; Jiang, Yin; Liao, Jinfeng

2016-05-01

In this paper we study the transport equation describing a dense system of gluons, in the small scattering angle approximation, taking into account medium-generated effective masses of the gluons. We focus on the case of overpopulated systems that are driven to Bose–Einstein condensation on their way to thermalization. Lastly, the presence of a mass modifies the dispersion relation of the gluon, as compared to the massless case, but it is shown that this does not change qualitatively the scaling behavior in the vicinity of the onset.

Gluon transport equation with effective mass and dynamical onset of Bose–Einstein condensation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blaizot, Jean-Paul; Jiang, Yin; Liao, Jinfeng

In this paper we study the transport equation describing a dense system of gluons, in the small scattering angle approximation, taking into account medium-generated effective masses of the gluons. We focus on the case of overpopulated systems that are driven to Bose–Einstein condensation on their way to thermalization. Lastly, the presence of a mass modifies the dispersion relation of the gluon, as compared to the massless case, but it is shown that this does not change qualitatively the scaling behavior in the vicinity of the onset.

Einstein-Cartan Gravity with Torsion Field Serving as an Origin for the Cosmological Constant or Dark Energy Density

NASA Astrophysics Data System (ADS)

Ivanov, A. N.; Wellenzohn, M.

2016-09-01

We analyse the Einstein-Cartan gravity in its standard form { R }=R+{{ K }}2, where { R } {and} R are the Ricci scalar curvatures in the Einstein-Cartan and Einstein gravity, respectively, and {{ K }}2 is the quadratic contribution of torsion in terms of the contorsion tensor { K }. We treat torsion as an external (or background) field and show that its contribution to the Einstein equations can be interpreted in terms of the torsion energy-momentum tensor, local conservation of which in a curved spacetime with an arbitrary metric or an arbitrary gravitational field demands a proportionality of the torsion energy-momentum tensor to a metric tensor, a covariant derivative of which vanishes owing to the metricity condition. This allows us to claim that torsion can serve as an origin for the vacuum energy density, given by the cosmological constant or dark energy density in the universe. This is a model-independent result that may explain the small value of the cosmological constant, which is a long-standing problem in cosmology. We show that the obtained result is valid also in the Poincaré gauge gravitational theory of Kibble, where the Einstein-Hilbert action can be represented in the same form: { R }=R+{{ K }}2.

Spherically symmetric vacuum solutions arising from trace dynamics modifications to gravitation

NASA Astrophysics Data System (ADS)

Adler, Stephen L.; Ramazanoğlu, Fethi M.

2015-12-01

We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action (derived from trace dynamics) that gives an alternative explanation of the origin of "dark energy". We give analytic and numerical results for the solutions of these equations, first in polar coordinates, and then in isotropic coordinates. General features of the static case are that: (i) there is no horizon, since g00 is nonvanishing for finite values of the polar radius, and only vanishes (in isotropic coordinates) at the internal singularity, (ii) the Ricci scalar R vanishes identically, and (iii) there is a physical singularity at cosmological distances. The large distance singularity may be an artifact of the static restriction, since we find that the behavior at large distances is altered in a time-dependent solution using the McVittie Ansatz.

Gravitational lensing effects of vacuum strings - Exact solutions

NASA Technical Reports Server (NTRS)

Gott, J. R., III

1985-01-01

Exact interior and exterior solutions to Einstein's field equations are derived for vacuum strings. The exterior solution for a uniform density vacuum string corresponds to a conical space while the interior solution is that of a spherical cap. For Mu equals 0-1/4 the external metric is ds-squared = -dt-squared + dr-squared + (1-4 Mu)-squared r-squared dphi-squared + dz-squared, where Mu is the mass per unit length in the string in Planck masses per Planck length. A maximum mass per unit length for a string is 6.73 x 10 to the 27th g/cm. It is shown that strings cause temperature fluctuations in the cosmic microwave background and produce equal brightness double QSO images separated by up to several minutes of arc. Formulae for lensing probabilities, image splittings, and time delays are derived for strings in a realistic cosmological setting. String searches using ST, the VLA, and the COBE satellite are discussed.

Einstein gravity with torsion induced by the scalar field

NASA Astrophysics Data System (ADS)

Özçelik, H. T.; Kaya, R.; Hortaçsu, M.

2018-06-01

We couple a conformal scalar field in (2+1) dimensions to Einstein gravity with torsion. The field equations are obtained by a variational principle. We could not solve the Einstein and Cartan equations analytically. These equations are solved numerically with 4th order Runge-Kutta method. From the numerical solution, we make an ansatz for the rotation parameter in the proposed metric, which gives an analytical solution for the scalar field for asymptotic regions.

Expanding space-time and variable vacuum energy

NASA Astrophysics Data System (ADS)

Parmeggiani, Claudio

2017-08-01

The paper describes a cosmological model which contemplates the presence of a vacuum energy varying, very slightly (now), with time. The constant part of the vacuum energy generated, some 6 Gyr ago, a deceleration/acceleration transition of the metric expansion; so now, in an aged Universe, the expansion is inexorably accelerating. The vacuum energy varying part is instead assumed to be eventually responsible of an acceleration/deceleration transition, which occurred about 14 Gyr ago; this transition has a dynamic origin: it is a consequence of the general relativistic Einstein-Friedmann equations. Moreover, the vacuum energy (constant and variable) is here related to the zero-point energy of some quantum fields (scalar, vector, or spinor); these fields are necessarily described in a general relativistic way: their structure depends on the space-time metric, typically non-flat. More precisely, the commutators of the (quantum field) creation/annihilation operators are here assumed to depend on the local value of the space-time metric tensor (and eventually of its curvature); furthermore, these commutators rapidly decrease for high momentum values and they reduce to the standard ones for a flat metric. In this way, the theory is ”gravitationally” regularized; in particular, the zero-point (vacuum) energy density has a well defined value and, for a non static metric, depends on the (cosmic) time. Note that this varying vacuum energy can be negative (Fermi fields) and that a change of its sign typically leads to a minimum for the metric expansion factor (a ”bounce”).

Derivation of the cut-off length from the quantum quadratic enhancement of a mass in vacuum energy constant Lambda

NASA Astrophysics Data System (ADS)

Fukushima, Kimichika; Sato, Hikaru

2018-04-01

Ultraviolet self-interaction energies in field theory sometimes contain meaningful physical quantities. The self-energies in such as classical electrodynamics are usually subtracted from the rest mass. For the consistent treatment of energies as sources of curvature in the Einstein field equations, this study includes these subtracted self-energies into vacuum energy expressed by the constant Lambda (used in such as Lambda-CDM). In this study, the self-energies in electrodynamics and macroscopic classical Einstein field equations are examined, using the formalisms with the ultraviolet cut-off scheme. One of the cut-off formalisms is the field theory in terms of the step-function-type basis functions, developed by the present authors. The other is a continuum theory of a fundamental particle with the same cut-off length. Based on the effectiveness of the continuum theory with the cut-off length shown in the examination, the dominant self-energy is the quadratic term of the Higgs field at a quantum level (classical self-energies are reduced to logarithmic forms by quantum corrections). The cut-off length is then determined to reproduce today's tiny value of Lambda for vacuum energy. Additionally, a field with nonperiodic vanishing boundary conditions is treated, showing that the field has no zero-point energy.

The Einstein-Vlasov System/Kinetic Theory.

PubMed

Andréasson, Håkan

2005-01-01

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, i.e. to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically, and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (i.e. fluid models). This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to good comprehension of kinetic theory in general relativity.

The Einstein-Vlasov System/Kinetic Theory.

PubMed

Andréasson, Håkan

2002-01-01

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, i.e. to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically, and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (i.e. fluid models). This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to good comprehension of kinetic theory in general relativity.

Static black hole and vacuum energy: thin shell and incompressible fluid

NASA Astrophysics Data System (ADS)

Ho, Pei-Ming; Matsuo, Yoshinori

2018-03-01

With the back reaction of the vacuum energy-momentum tensor consistently taken into account, we study static spherically symmetric black-hole-like solutions to the semi-classical Einstein equation. The vacuum energy is assumed to be given by that of 2-dimensional massless scalar fields, as a widely used model in the literature for black holes. The solutions have no horizon. Instead, there is a local minimum in the radius. We consider thin shells as well as incompressible fluid as the matter content of the black-hole-like geometry. The geometry has several interesting features due to the back reaction of vacuum energy. In particular, Buchdahl's inequality can be violated without divergence in pressure, even if the surface is below the Schwarzschild radius. At the same time, the surface of the star can not be far below the Schwarzschild radius for a density not much higher than the Planck scale, and the proper distance from its surface to the origin can be very short even for very large Schwarzschild radius. The results also imply that, contrary to the folklore, in principle the Boulware vacuum can be physical for black holes.

Piecewise linear emulator of the nonlinear Schrödinger equation and the resulting analytic solutions for Bose-Einstein condensates.

PubMed

Theodorakis, Stavros

2003-06-01

We emulate the cubic term Psi(3) in the nonlinear Schrödinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a delta function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Psi(3) one. In particular, it can be used for the nonlinear Schrödinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions.

Scalar field as a Bose-Einstein condensate?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Castellanos, Elías; Escamilla-Rivera, Celia; Macías, Alfredo

We discuss the analogy between a classical scalar field with a self-interacting potential, in a curved spacetime described by a quasi-bounded state, and a trapped Bose-Einstein condensate. In this context, we compare the Klein-Gordon equation with the Gross-Pitaevskii equation. Moreover, the introduction of a curved background spacetime endows, in a natural way, an equivalence to the Gross-Pitaevskii equation with an explicit confinement potential. The curvature also induces a position dependent self-interaction parameter. We exploit this analogy by means of the Thomas-Fermi approximation, commonly used to describe the Bose-Einstein condensate, in order to analyze the quasi bound scalar field distribution surroundingmore » a black hole.« less

Spacetime dynamics of a Higgs vacuum instability during inflation

DOE PAGES

East, William E.; Kearney, John; Shakya, Bibhushan; ...

2017-01-31

A remarkable prediction of the Standard Model is that, in the absence of corrections lifting the energy density, the Higgs potential becomes negative at large field values. If the Higgs field samples this part of the potential during inflation, the negative energy density may locally destabilize the spacetime. Here, we use numerical simulations of the Einstein equations to study the evolution of inflation-induced Higgs fluctuations as they grow towards the true (negative-energy) minimum. Our simulations show that forming a single patch of true vacuum in our past light cone during inflation is incompatible with the existence of our Universe; themore » boundary of the true vacuum region grows outward in a causally disconnected manner from the crunching interior, which forms a black hole. We also find that these black hole horizons may be arbitrarily elongated—even forming black strings—in violation of the hoop conjecture. Furthermore, by extending the numerical solution of the Fokker-Planck equation to the exponentially suppressed tails of the field distribution at large field values, we derive a rigorous correlation between a future measurement of the tensor-to-scalar ratio and the scale at which the Higgs potential must receive stabilizing corrections in order for the Universe to have survived inflation until today.« less

A modification of Einstein-Schrödinger theory that contains both general relativity and electrodynamics

NASA Astrophysics Data System (ADS)

Shifflett, J. A.

2008-08-01

We modify the Einstein-Schrödinger theory to include a cosmological constant Λ z which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant Λ z is assumed to be nearly cancelled by Schrödinger’s cosmological constant Λ b which multiplies the nonsymmetric fundamental tensor, such that the total Λ = Λ z + Λ b matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as | Λ z | → ∞. For | Λ z | ~ 1/(Planck length)2 the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are < 10-16 of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein-Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. This fixes a problem of the original Einstein-Schrödinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner-Nordström solution except for additional terms which are ~10-66 of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory.

Matter rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates.

PubMed

Sun, Wen-Rong; Wang, Lei

2018-01-01

To show the existence and properties of matter rogue waves in an F =1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F =1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

Matter rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Sun, Wen-Rong; Wang, Lei

2018-01-01

To show the existence and properties of matter rogue waves in an F=1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F=1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.

BOOK REVIEW: Einsteins Kosmos. Untersuchungen zur Geschichte der Kosmologie Relativitatstheorie und zu Einsteins Wirken und Nachwirken

NASA Astrophysics Data System (ADS)

Sterken, C.; Duerbeck, H. W.; Dick, W. R.

2006-12-01

Schwarzschild's cosmological speculations, and wonders why some people do immediately grasp the meaning and consequence of newly proposed doctrines, whereas the bulk of the contemporaneous scientists respond in a rather low profile. T. Jung reviews Einstein's contribution to cosmology, leading to the Friedmann-Einstein and Einstein-de Sitter universes (with a detailed Appendix on the Friedmann-Lemaitre cosmology), and also presents the cosmological work of Selety, and his correspondence with Einstein. In a subsequent paper, H.-J. Schmidt comments on Einstein's criticism on de Sitter's solution of the Einstein field equations. Controversies with Einstein are elaborated by G. Singer (on Friedmann) and by K. Roessler (on Lemaitre). J. Renn and T. Sauer discuss Mandl's role in the publication history of Einstein's papers, notably Einstein's short paper on gravitational lensing. Finally, the book concludes with a contribution by D.B. Herrmann about the relationship between Einstein and Archenhold Observatory (where Einstein gave his first Berlin popular lecture in 1915), the transcription of H.-J. Treder's 1979 public address at the Einstein memorial plaque, and an inventory list of about 50 Einstein memorabilia - monuments, busts, plaques - compiled by W.R. Dick. This book is based on ideas approached in a historical context from the individual perspective of the authors. It is a real treasure trove of information and basic references on the history of GR, and it also covers quite some grounds with mathematical equations.

Gravitational baryogenesis in running vacuum models

NASA Astrophysics Data System (ADS)

Oikonomou, V. K.; Pan, Supriya; Nunes, Rafael C.

2017-08-01

We study the gravitational baryogenesis mechanism for generating baryon asymmetry in the context of running vacuum models. Regardless of whether these models can produce a viable cosmological evolution, we demonstrate that they produce a nonzero baryon-to-entropy ratio even if the universe is filled with conformal matter. This is a sound difference between the running vacuum gravitational baryogenesis and the Einstein-Hilbert one, since in the latter case, the predicted baryon-to-entropy ratio is zero. We consider two well known and most used running vacuum models and show that the resulting baryon-to-entropy ratio is compatible with the observational data. Moreover, we also show that the mechanism of gravitational baryogenesis may constrain the running vacuum models.

α-quantized Einstein masses for leptons, quarks, hadrons, gauge bosons, and Higgs constants

NASA Astrophysics Data System (ADS)

Mac Gregor, Malcolm

2011-11-01

The Einstein particle mass ɛi is defined by the equation ɛi = Ei / c^2. The basic particle ground states have unique additive Einstein masses (energies), and they interleave in α-quantized (α-1 = 137) energy plots to form distinctive excitation patterns. The ɛu,d,s,c,b,t Einstein masses are constituent-quark masses. Particle generation proceeds via ``α-boosted'' boson, fermion, and gauge-boson ``unit masses,'' which are ``bundled'' together to form particles and quarks. The Einstein mass equations extend throughout the entire range of particle masses. Lederman and HillootnotetextL. M. Lederman and C. T. Hill, Symmetry (Prometheus Books, Amherst, 2004), p. 282. note that the scalar Higgs and Fermi fields are at the 175 GeV energy scale of the top quark t, and they suggest the Higgs coupling constant equation ge=me/mt = 0.0000029, which matches the Einstein mass expression ge=α^2/18.

A Classical Based Derivation of Time Dilation Providing First Order Accuracy to Schwarzschild's Solution of Einstein's Field Equations

NASA Astrophysics Data System (ADS)

Austin, Rickey W.

In Einstein's theory of Special Relativity (SR), one method to derive relativistic kinetic energy is via applying the classical work-energy theorem to relativistic momentum. This approach starts with a classical based work-energy theorem and applies SR's momentum to the derivation. One outcome of this derivation is relativistic kinetic energy. From this derivation, it is rather straight forward to form a kinetic energy based time dilation function. In the derivation of General Relativity a common approach is to bypass classical laws as a starting point. Instead a rigorous development of differential geometry and Riemannian space is constructed, from which classical based laws are derived. This is in contrast to SR's approach of starting with classical laws and applying the consequences of the universal speed of light by all observers. A possible method to derive time dilation due to Newtonian gravitational potential energy (NGPE) is to apply SR's approach to deriving relativistic kinetic energy. It will be shown this method gives a first order accuracy compared to Schwarzschild's metric. The SR's kinetic energy and the newly derived NGPE derivation are combined to form a Riemannian metric based on these two energies. A geodesic is derived and calculations compared to Schwarzschild's geodesic for an orbiting test mass about a central, non-rotating, non-charged massive body. The new metric results in high accuracy calculations when compared to Einsteins General Relativity's prediction. The new method provides a candidate approach for starting with classical laws and deriving General Relativity effects. This approach mimics SR's method of starting with classical mechanics when deriving relativistic equations. As a compliment to introducing General Relativity, it provides a plausible scaffolding method from classical physics when teaching introductory General Relativity. A straight forward path from classical laws to General Relativity will be derived. This derivation

Diffusion coefficients in organic-water solutions and comparison with Stokes-Einstein predictions

NASA Astrophysics Data System (ADS)

Evoy, E.; Kamal, S.; Bertram, A. K.

2017-12-01

Diffusion coefficients of organic species in particles containing secondary organic material (SOM) are necessary for predicting the growth and reactivity of these particles in the atmosphere. Previously, the Stokes-Einstein equation combined with viscosity measurements have been used to predict these diffusion coefficients. However, the accuracy of the Stokes-Einstein equation for predicting diffusion coefficients in SOM-water particles has not been quantified. To test the Stokes-Einstein equation, diffusion coefficients of fluorescent organic probe molecules were measured in citric acid-water and sorbitol-water solutions. These solutions were used as proxies for SOM-water particles found in the atmosphere. Measurements were performed as a function of water activity, ranging from 0.26-0.86, and as a function of viscosity ranging from 10-3 to 103 Pa s. Diffusion coefficients were measured using fluorescence recovery after photobleaching. The measured diffusion coefficients were compared with predictions made using the Stokes-Einstein equation combined with literature viscosity data. Within the uncertainties of the measurements, the measured diffusion coefficients agreed with the predicted diffusion coefficients, in all cases.

A distinguishing gravitational property for gravitational equation in higher dimensions

NASA Astrophysics Data System (ADS)

Dadhich, Naresh

2016-03-01

It is well known that Einstein gravity is kinematic (meaning that there is no non-trivial vacuum solution; i.e. the Riemann tensor vanishes whenever the Ricci tensor does so) in 3 dimension because the Riemann tensor is entirely given in terms of the Ricci tensor. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one Nth order term in the action) gravity for which the Nth order Lovelock-Riemann tensor is indeed given in terms of the corresponding Ricci tensor for all odd, d=2N+1, dimensions. This feature of gravity is realized only in higher dimensions and it uniquely picks out pure Lovelock gravity from all other generalizations of Einstein gravity. It serves as a good distinguishing and guiding criterion for the gravitational equation in higher dimensions.

Infinite-Dimensional Symmetry Algebras as a Help Toward Solutions of the Self-Dual Field Equations with One Killing Vector

NASA Astrophysics Data System (ADS)

Finley, Daniel; McIver, John K.

2002-12-01

The sDiff(2) Toda equation determines all self-dual, vacuum solutions of the Einstein field equations with one rotational Killing vector. Some history of the searches for non-trivial solutions is given, including those that begin with the limit as n → ∞ of the An Toda lattice equations. That approach is applied here to the known prolongation structure for the Toda lattice, hoping to use Bäcklund transformations to generate new solutions. Although this attempt has not yet succeeded, new faithful (tangent-vector) realizations of A∞ are described, and a direct approach via the continuum Lie algebras of Saveliev and Leznov is given.

Effects of quadratic coupling and squeezed vacuum injection in an optomechanical cavity assisted with a Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Dalafi, A.; Naderi, M. H.; Motazedifard, Ali

2018-04-01

We investigate theoretically a hybrid system consisting of a Bose-Einstein condensate (BEC) trapped inside a laser-driven membrane-in-the-middle optomechanical cavity assisted with squeezed vacuum injection whose moving membrane interacts both linearly and quadratically with the radiation pressure of the cavity. It is shown that such a hybrid system is very suitable for generating strong quadrature squeezing in the mechanical mode of the membrane and the Bogoliubov mode of the BEC in the unresolved sideband regime. More interestingly, by choosing a suitable sign for the quadratic optomechanical coupling (QOC), one can achieve a very high degree of squeezing in the mechanical mode and a strong entanglement between the mechanical and atomic modes without the necessity of using squeezed light injection. Furthermore, the QOC changes the effective oscillation frequencies of both the mechanical and the atomic modes and affects their relaxation times. It can also make the system switch from optical bistability to tristability.

The Einstein-Vlasov System/Kinetic Theory.

PubMed

Andréasson, Håkan

2011-01-01

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.

On a remarkable electromagnetic field in the Einstein Universe

NASA Astrophysics Data System (ADS)

Kopiński, Jarosław; Natário, José

2017-06-01

We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the 3-sphere S^3. The conformal equivalence between Minkowski's spacetime and (a region of) the Einstein cylinder is then exploited in order to obtain a knotted, finite energy, radiating solution of the Maxwell equations in flat spacetime. We also discuss similar electromagnetic fields in expanding closed Friedmann models, and compute the matter content of such configurations.

Dutch museum marks Einstein anniversary

NASA Astrophysics Data System (ADS)

van Calmthout, Matijn

2016-01-01

A new painting of Albert Einstein's field equation from his 1915 general theory of relativity was unveiled in a ceremony in November 2015 by the Dutch physicist Robbert Dijkgraaf, who is director of the Princeton Institute for Advanced Study in the US.

Newton to Einstein — dust to dust

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kopp, Michael; Uhlemann, Cora; Haugg, Thomas, E-mail: michael.kopp@physik.lmu.de, E-mail: cora.uhlemann@physik.lmu.de, E-mail: thomas.haugg@physik.lmu.de

We investigate the relation between the standard Newtonian equations for a pressureless fluid (dust) and the Einstein equations in a double expansion in small scales and small metric perturbations. We find that parts of the Einstein equations can be rewritten as a closed system of two coupled differential equations for the scalar and transverse vector metric perturbations in Poisson gauge. It is then shown that this system is equivalent to the Newtonian system of continuity and Euler equations. Brustein and Riotto (2011) conjectured the equivalence of these systems in the special case where vector perturbations were neglected. We show thatmore » this approach does not lead to the Euler equation but to a physically different one with large deviations already in the 1-loop power spectrum. We show that it is also possible to consistently set to zero the vector perturbations which strongly constrains the allowed initial conditions, in particular excluding Gaussian ones such that inclusion of vector perturbations is inevitable in the cosmological context. In addition we derive nonlinear equations for the gravitational slip and tensor perturbations, thereby extending Newtonian gravity of a dust fluid to account for nonlinear light propagation effects and dust-induced gravitational waves.« less

BOOK REVIEW: A Student's Guide to Einstein's Major Papers A Student's Guide to Einstein's Major Papers

NASA Astrophysics Data System (ADS)

Janssen, Michel

2013-12-01

just 26 pages (not counting six pages of notes and references) covers everything from Copernicus, Galileo, Kepler and Newton to Maxwell and Lorentz to Einstein's early biography to a cardboard version of Popper versus Kuhn, is too superficial to be useful for such a course. To a lesser extent, this is also true for chapter 6, which compresses the development of quantum theory after Einstein's 1905 paper into 20 pages (plus seven pages of notes and references) and for chapter 7, a brief epilogue. However, this is not my main worry. One could easily supplement or even replace the bookends of the volume with other richer sources and use this volume mainly for its excellent detailed commentaries on some Einstein classics in the four chapters in between. My more serious reservation about the use of the volume as a whole in a history of physics course, ironically, comes from the exact same feature that made me whole-heartedly recommend its core chapters for physics courses. This is especially true for the chapters on special and general relativity. How useful is it for a student to go through, in as much detail as this volume provides, the Lorentz transformation of Maxwell's equations in vector form? I can see how a student in an E&M class (with a section on special relativity) might benefit from this exercise. The clumsiness of the calculations in vector form by Lorentz and Einstein could help a student encountering Maxwell's equations in tensor form for the first time appreciate the advantages of the latter formalism. Similarly, it would be useful for a student in a GR class to go through the basics of tensor calculus in the old-fashioned but not inelegant mathematical introduction of Einstein's 1916 review article on general relativity. This could reinforce mastery of material that a student in a GR class will have to learn anyway (though Einstein's presentation of the mathematics of both special and general relativity in The Meaning of Relativity would seem to be more

Bose–Einstein condensates and scalar fields; exploring the similitudes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Castellanos, E.; Macías, A.; Núñez, D.

We analyze the the remarkable analogy between the classical Klein–Gordon equation for a test scalar field in a flat and also in a curved background, and the Gross–Pitaevskii equation for a Bose–Einstein condensate trapped by an external potential. We stress here that the solution associated with the Klein–Gordon equation (KG) in a flat space time has the same mathematical structure, under certain circumstances, to those obtained for the Gross–Pitaevskii equation, that is, a static soliton solution. Additionally, Thomas–Fermi approximation is applied to the 3–dimensional version of this equation, in order to calculate some thermodynamical properties of the system in curvedmore » a space–time back ground. Finally, we stress the fact that a gravitational background provides, in some cases, a kind of confining potential for the scalar field, allowing us to remarks even more the possible connection between scalar fields and the phenomenon of Bose–Einstein condensation.« less

Periodic, complexiton solutions and stability for a (2+1)-dimensional variable-coefficient Gross-Pitaevskii equation in the Bose-Einstein condensation

NASA Astrophysics Data System (ADS)

Yin, Hui-Min; Tian, Bo; Zhao, Xin-Chao

2018-06-01

This paper presents an investigation of a (2 + 1)-dimensional variable-coefficient Gross-Pitaevskii equation in the Bose-Einstein condensation. Periodic and complexiton solutions are obtained. Solitons solutions are also gotten through the periodic solutions. Numerical solutions via the split step method are stable. Effects of the weak and strong modulation instability on the solitons are shown: the weak modulation instability permits an observable soliton, and the strong one overwhelms its development.

Electron dynamics inside a vacuum tube diode through linear differential equations

NASA Astrophysics Data System (ADS)

González, Gabriel; Orozco, Fco. Javier González; Orozco

2014-04-01

In this paper we analyze the motion of charged particles in a vacuum tube diode by solving linear differential equations. Our analysis is based on expressing the volume charge density as a function of the current density and coordinates only, i.e. ρ=ρ(J,z), while in the usual scheme the volume charge density is expressed as a function of the current density and electrostatic potential, i.e. ρ=ρ(J,V). We show that, in the case of slow varying charge density, the space-charge-limited current is reduced up to 50%. Our approach gives the well-known behavior of the classical current density proportional to the three-halves power of the bias potential and inversely proportional to the square of the gap distance between electrodes, and does not require the solution of the nonlinear differential equation normally associated with the Child-Langmuir formulation.

Finding Horndeski theories with Einstein gravity limits

DOE Office of Scientific and Technical Information (OSTI.GOV)

McManus, Ryan; Lombriser, Lucas; Peñarrubia, Jorge, E-mail: ryanm@roe.ac.uk, E-mail: llo@roe.ac.uk, E-mail: jorpega@roe.ac.uk

The Horndeski action is the most general scalar-tensor theory with at most second-order derivatives in the equations of motion, thus evading Ostrogradsky instabilities and making it of interest when modifying gravity at large scales. To pass local tests of gravity, these modifications predominantly rely on nonlinear screening mechanisms that recover Einstein's Theory of General Relativity in regions of high density. We derive a set of conditions on the four free functions of the Horndeski action that examine whether a specific model embedded in the action possesses an Einstein gravity limit or not. For this purpose, we develop a new andmore » surprisingly simple scaling method that identifies dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in the modified action. This enables us to find regimes where nonlinear terms dominate and Einstein's field equations are recovered to leading order. Together with an efficient approximation of the scalar field profile, one can then further evaluate whether these limits can be attributed to a genuine screening effect. For illustration, we apply the analysis to both a cubic galileon and a chameleon model as well as to Brans-Dicke theory. Finally, we emphasise that the scaling method also provides a natural approach for performing post-Newtonian expansions in screened regimes.« less

The Evolution of Hyperedge Cardinalities and Bose-Einstein Condensation in Hypernetworks.

PubMed

Guo, Jin-Li; Suo, Qi; Shen, Ai-Zhong; Forrest, Jeffrey

2016-09-27

To depict the complex relationship among nodes and the evolving process of a complex system, a Bose-Einstein hypernetwork is proposed in this paper. Based on two basic evolutionary mechanisms, growth and preference jumping, the distribution of hyperedge cardinalities is studied. The Poisson process theory is used to describe the arrival process of new node batches. And, by using the Poisson process theory and a continuity technique, the hypernetwork is analyzed and the characteristic equation of hyperedge cardinalities is obtained. Additionally, an analytical expression for the stationary average hyperedge cardinality distribution is derived by employing the characteristic equation, from which Bose-Einstein condensation in the hypernetwork is obtained. The theoretical analyses in this paper agree with the conducted numerical simulations. This is the first study on the hyperedge cardinality in hypernetworks, where Bose-Einstein condensation can be regarded as a special case of hypernetworks. Moreover, a condensation degree is also discussed with which Bose-Einstein condensation can be classified.

Einstein Revisited - Gravity in Curved Spacetime Without Event Horizons

NASA Astrophysics Data System (ADS)

Leiter, Darryl

2000-04-01

In terms of covariant derivatives with respect to flat background spacetimes upon which the physical curved spacetime is imposed (1), covariant conservation of energy momentum requires, via the Bianchi Identity, that the Einstein tensor be equated to the matter energy momentum tensor. However the Einstein tensor covariantly splits (2) into two tensor parts: (a) a term proportional to the gravitational stress energy momentum tensor, and (b) an anti-symmetric tensor which obeys a covariant 4-divergence identity called the Freud Identity. Hence covariant conservation of energy momentum requires, via the Freud Identity, that the Freud tensor be equal to a constant times the matter energy momentum tensor. The resultant field equations (3) agree with the Einstein equations to first order, but differ in higher orders (4) such that black holes are replaced by "red holes" i.e., dense objects collapsed inside of their photon orbits with no event horizons. (1) Rosen, N., (1963), Ann. Phys. v22, 1; (2) Rund, H., (1991), Alg. Grps. & Geom. v8, 267; (3) Yilmaz, Hl, (1992), Nuo. Cim. v107B, 946; (4) Roberstson, S., (1999),Ap.J. v515, 365.

Exact solutions to quadratic gravity

NASA Astrophysics Data System (ADS)

Pravda, V.; Pravdová, A.; Podolský, J.; Švarc, R.

2017-04-01

Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is necessarily a Kundt spacetime. This will considerably simplify the search for new non-Einstein solutions. Similarly, a vacuum solution to quadratic gravity with traceless Ricci type III and aligned Weyl tensor of Petrov type II or more special is again necessarily a Kundt spacetime. Then we study the general role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one nonlinear partial differential equation for a conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. In particular, we show that all geometries conformal to Kundt are either Kundt or Robinson-Trautman, and we provide some explicit Kundt and Robinson-Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.

Non-naturally reductive Einstein metrics on exceptional Lie groups

NASA Astrophysics Data System (ADS)

Chrysikos, Ioannis; Sakane, Yusuke

2017-06-01

Given an exceptional compact simple Lie group G we describe new left-invariant Einstein metrics which are not naturally reductive. In particular, we consider fibrations of G over flag manifolds with a certain kind of isotropy representation and we construct the Einstein equation with respect to the induced left-invariant metrics. Then we apply a technique based on Gröbner bases and classify the real solutions of the associated algebraic systems. For the Lie group G2 we obtain the first known example of a left-invariant Einstein metric, which is not naturally reductive. Moreover, for the Lie groups E7 and E8, we conclude that there exist non-isometric non-naturally reductive Einstein metrics, which are Ad(K) -invariant by different Lie subgroups K.

Einstein's conversion from his static to an expanding universe

NASA Astrophysics Data System (ADS)

Nussbaumer, Harry

2014-02-01

In 1917 Einstein initiated modern cosmology by postulating, based on general relativity, a homogenous, static, spatially curved universe. To counteract gravitational contraction he introduced the cosmological constant. In 1922 Alexander Friedman showed that Albert Einstein's fundamental equations also allow dynamical worlds, and in 1927 Georges Lemaître, backed by observational evidence, concluded that our universe was expanding. Einstein impetuously rejected Friedman's as well as Lemaître's findings. However, in 1931 he retracted his former static model in favour of a dynamic solution. This investigation follows Einstein on his hesitating path from a static to the expanding universe. Contrary to an often advocated belief the primary motive for his switch was not observational evidence, but the realisation that his static model was unstable.

Einstein's Cosmos (German Title: Einsteins Kosmos)

NASA Astrophysics Data System (ADS)

Duerbeck, Hilmar W.; Dick, Wolfgang R.

The different contributions of the present volume illuminate the interaction between Einstein and his colleagues when the foundations of modern cosmology were laid: First, the relativistic effects in the solar system, the gravitational redshift in the solar spectrum, and Einstein's relations with Freundlich and Eddington. Second, the cosmological models of Einstein, de Sitter, Friedmann, and Lemaître, which were discussed controversely till the end of the 1920s. Other scientists have also widened or critically questioned Einstein's insight and knowledge: Schwarzschild, Selety, Silberstein, and Mandl, whose life and work is discussed in separate articles. In those days, politics more than ever in history had influenced the lifes of scientists. Therefore, some comments on the ``political cosmos'' that has influenced decisively Einstein's life are also given. A special role in popularizing Einstein's world view was played by Archenhold Observatory in Berlin. A list of Einstein memorial places and a bibliographic list conclude the present book. All papers are written in German, and have English abstracts.

Einstein and a century of time

NASA Astrophysics Data System (ADS)

Raine, D. J.

2005-09-01

suggests that Mach's principle may yet have a surprising role in expressing the fact that the Universe contains sufficient matter to exist as a classical system: that is, that it contains sufficient material degrees of freedom to allow quantum decoherence to occur. It would at least be a nice irony if Mach's principle turned out to be a necessary quantum condition for the existence of a classical universe! Coming now to the papers in this special feature, these include several that treat historical aspects of relativity. Brown offers us a novel insight into Einstein's ambivalence about the status of special relativity in providing a mechanism for the contraction hypothesis. Trainer looks at the way in which Einstein presented a brief account of relativity in a lecture that he gave in Glasgow in 1933. Galvangno and Giribet look at Einstein's approach to the representation of particles within general relativity, or variants thereof, while Battimelli provides an account of attempts at unification of electromagnetism and relativity from the point of view of the origin of mass. In their contribution, Guerra and de Abreu look again at the relationship between the constancy of the speed of light and the nature of time that was central to Einstein's thinking. Next we come to a group of papers that look at educational issues. Einstein's equation E = mc2 is now iconic even if general knowledge quizzes that ask what the c stands for miss the entire point of the equation! Thomas starts from the way in which perceptions of relativity still focus on this equation as the essential ingredient of nuclear power and the need to disabuse even students of physics of this notion. He also looks at how we can in fact demonstrate the significance of the equation to a lay audience. I have added a short note on friction, another topic that confuses teachers and students alike, that throws up problems to which the solutions are contained in Einstein's Brownian motion paper. The Open University in the

All ASD complex and real 4-dimensional Einstein spaces with Λ≠0 admitting a nonnull Killing vector

NASA Astrophysics Data System (ADS)

Chudecki, Adam

2016-12-01

Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant Λ equipped with a nonnull Killing vector are considered. It is shown that any conformally nonflat metric of such spaces can be always brought to a special form and the Einstein field equations can be reduced to the Boyer-Finley-Plebański equation (Toda field equation). Some alternative forms of the metric are discussed. All possible real slices (neutral, Euclidean and Lorentzian) of ASD complex Einstein spaces with Λ≠0 admitting a nonnull Killing vector are found.

Induced matter brane gravity and Einstein static universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydarzade, Y.; Darabi, F., E-mail: heydarzade@azaruniv.edu, E-mail: f.darabi@azaruniv.edu

We investigate stability of the Einstein static universe against the scalar, vector and tensor perturbations in the context of induced matter brane gravity. It is shown that in the framework of this model, the Einstein static universe has a positive spatial curvature. In contrast to the classical general relativity, it is found that a stable Einstein static universe against the scalar perturbations does exist provided that the variation of time dependent geometrical equation of state parameter is proportional to the minus of the variation of the scale factor, δ ω{sub g}(t) = −Cδ a(t). We obtain neutral stability against the vector perturbations, and themore » stability against the tensor perturbations is guaranteed due to the positivity of the spatial curvature of the Einstein static universe in induced matter brane gravity.« less

Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

NASA Astrophysics Data System (ADS)

Cao, ChunJun; Carroll, Sean M.

2018-04-01

We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.

Superenergy flux of Einstein-Rosen waves

NASA Astrophysics Data System (ADS)

Domínguez, P. J.; Gallegos, A.; Macías-Díaz, J. E.; Vargas-Rodríguez, H.

In this work, we consider the propagation speed of the superenergy flux associated to the Einstein-Rosen cylindrical waves propagating in vacuum and over the background of the gravitational field of an infinitely long mass line distribution. The velocity of the flux is determined considering the reference frame in which the super-Poynting vector vanishes. This reference frame is then considered as comoving with the flux. The explicit expressions for the velocities are given with respect to a reference frame at rest with the symmetry axis.

Einstein's Approach to Statistical Mechanics: The 1902-04 Papers

NASA Astrophysics Data System (ADS)

Peliti, Luca; Rechtman, Raúl

2017-05-01

We summarize the papers published by Einstein in the Annalen der Physik in the years 1902-1904 on the derivation of the properties of thermal equilibrium on the basis of the mechanical equations of motion and of the calculus of probabilities. We point out the line of thought that led Einstein to an especially economical foundation of the discipline, and to focus on fluctuations of the energy as a possible tool for establishing the validity of this foundation. We also sketch a comparison of Einstein's approach with that of Gibbs, suggesting that although they obtained similar results, they had different motivations and interpreted them in very different ways.

Static vacuum solutions on curved space-times with torsion

NASA Astrophysics Data System (ADS)

Shabani, Hamid; Ziaie, Amir Hadi

2018-06-01

The Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity naturally extends Einstein’s general relativity (GR) to include intrinsic angular momentum (spin) of matter. The main feature of this theory consists of an algebraic relation between space-time torsion and spin of matter, which indeed deprives the torsion of its dynamical content. The Lagrangian of ECKS gravity is proportional to the Ricci curvature scalar constructed out of a general affine connection so that owing to the influence of matter energy-momentum and spin, curvature and torsion are produced and interact only through the space-time metric. In the absence of spin, the space-time torsion vanishes and the theory reduces to GR. It is however possible to have torsion propagation in vacuum by resorting to a model endowed with a nonminimal coupling between curvature and torsion. In the present work we try to investigate possible effects of the higher order terms that can be constructed from space-time curvature and torsion, as the two basic constituents of Riemann-Cartan geometry. We consider Lagrangians that include fourth-order scalar invariants from curvature and torsion and then investigate the resulting field equations. The solutions that we find show that there could exist, even in vacuum, nontrivial static space-times that admit both black holes and naked singularities.

Bose-Einstein condensation of light: general theory.

PubMed

Sob'yanin, Denis Nikolaevich

2013-08-01

A theory of Bose-Einstein condensation of light in a dye-filled optical microcavity is presented. The theory is based on the hierarchical maximum entropy principle and allows one to investigate the fluctuating behavior of the photon gas in the microcavity for all numbers of photons, dye molecules, and excitations at all temperatures, including the whole critical region. The master equation describing the interaction between photons and dye molecules in the microcavity is derived and the equivalence between the hierarchical maximum entropy principle and the master equation approach is shown. The cases of a fixed mean total photon number and a fixed total excitation number are considered, and a much sharper, nonparabolic onset of a macroscopic Bose-Einstein condensation of light in the latter case is demonstrated. The theory does not use the grand canonical approximation, takes into account the photon polarization degeneracy, and exactly describes the microscopic, mesoscopic, and macroscopic Bose-Einstein condensation of light. Under certain conditions, it predicts sub-Poissonian statistics of the photon condensate and the polarized photon condensate, and a universal relation takes place between the degrees of second-order coherence for these condensates. In the macroscopic case, there appear a sharp jump in the degrees of second-order coherence, a sharp jump and kink in the reduced standard deviations of the fluctuating numbers of photons in the polarized and whole condensates, and a sharp peak, a cusp, of the Mandel parameter for the whole condensate in the critical region. The possibility of nonclassical light generation in the microcavity with the photon Bose-Einstein condensate is predicted.

Hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit: General formalism and perturbations analysis

NASA Astrophysics Data System (ADS)

Suárez, Abril; Chavanis, Pierre-Henri

2015-07-01

Using a generalization of the Madelung transformation, we derive the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit. We consider a complex self-interacting scalar field with a λ |φ |4 potential. We study the evolution of the spatially homogeneous background in the fluid representation and derive the linearized equations describing the evolution of small perturbations in a static and in an expanding Universe. We compare the results with simplified models in which the gravitational potential is introduced by hand in the Klein-Gordon equation, and assumed to satisfy a (generalized) Poisson equation. Nonrelativistic hydrodynamic equations based on the Schrödinger-Poisson equations or on the Gross-Pitaevskii-Poisson equations are recovered in the limit c →+∞. We study the evolution of the perturbations in the matter era using the nonrelativistic limit of our formalism. Perturbations whose wavelength is below the Jeans length oscillate in time while perturbations whose wavelength is above the Jeans length grow linearly with the scale factor as in the cold dark matter model. The growth of perturbations in the scalar field model is substantially faster than in the cold dark matter model. When the wavelength of the perturbations approaches the cosmological horizon (Hubble length), a relativistic treatment is mandatory. In that case, we find that relativistic effects attenuate or even prevent the growth of perturbations. This paper exposes the general formalism and provides illustrations in simple cases. Other applications of our formalism will be considered in companion papers.

Schwinger's Approach to Einstein's Gravity

NASA Astrophysics Data System (ADS)

Milton, Kim

2012-05-01

Albert Einstein was one of Julian Schwinger's heroes, and Schwinger was greatly honored when he received the first Einstein Prize (together with Kurt Godel) for his work on quantum electrodynamics. Schwinger contributed greatly to the development of a quantum version of gravitational theory, and his work led directly to the important work of (his students) Arnowitt, Deser, and DeWitt on the subject. Later in the 1960's and 1970's Schwinger developed a new formulation of quantum field theory, which he dubbed Source Theory, in an attempt to get closer contact to phenomena. In this formulation, he revisited gravity, and in books and papers showed how Einstein's theory of General Relativity emerged naturally from one physical assumption: that the carrier of the gravitational force is a massless, helicity-2 particle, the graviton. (There has been a minor dispute whether gravitational theory can be considered as the massless limit of a massive spin-2 theory; Schwinger believed that was the case, while Van Dam and Veltman concluded the opposite.) In the process, he showed how all of the tests of General Relativity could be explained simply, without using the full machinery of the theory and without the extraneous concept of curved space, including such effects as geodetic precession and the Lense-Thirring effect. (These effects have now been verified by the Gravity Probe B experiment.) This did not mean that he did not accept Einstein's equations, and in his book and full article on the subject, he showed how those emerge essentially uniquely from the assumption of the graviton. So to speak of Schwinger versus Einstein is misleading, although it is true that Schwinger saw no necessity to talk of curved spacetime. In this talk I will lay out Schwinger's approach, and the connection to Einstein's theory.

Black-Hole Solutions to Einstein's Equations in the Presence of Matter and Modifications of Gravitation in Extra Dimensions

NASA Astrophysics Data System (ADS)

Goutéraux, B.

2010-11-01

In this thesis, we wish to examine the black-hole solutions of modified gravity theories inspired by String Theory or Cosmology. Namely, these modifications will take the guise of additional gauge and scalar fields for the so-called Einstein-Maxwell-Dilaton theories with an exponential Liouville potential; and of extra spatial dimensions for Einstein-Gauss-Bonnet theories. The black-hole solutions of EMD theories as well as their integrability are reviewed. One of the main results is that a master equation is obtained in the case of planar horizon topology, which allows to completely integrate the problem for s special relationship between the couplings. We also classify existing solutions. We move on to the study of Gauss-Bonnet black holes, focusing on the six-dimensional case. It is found that the Gauss-Bonnet coupling exposes the Weyl tensor of the horizon to the dynamics, severely restricting the Einstein spaces admissible and effectively lifting some of the degeneracy on the horizon topology. We then turn to the study of the thermodynamic properties of black holes, in General Relativity as well as in EMD theories. For the latter, phase transitions may be found in the canonical ensemble, which resemble the phase transitions for Reissner-Nordström black holes. Generically, we find that the thermodynamic properties (stability, order of phase transitions) depend crucially on the values of the EMD coupling constants. Finally, we interpret our planar EMD solutions holographically as Infra-Red geometries through the AdS/CFT correspondence, taking into account various validity constraints. We also compute AC and DC conductivities as applications to Condensed Matter Systems, and find some properties characteristic of strange metal behaviour.

Einstein and Einstein A: A Study in Crater Morphology

NASA Image and Video Library

2017-12-08

NASA image release May 14, 2010 Einstein and Einstein A: A Study in Crater Morphology Located on the western limb of the Moon, Einstein and Einstein A craters (16.3oN, 271.3oE ) are only visible to Earth-based observers during certain lunar lighting and orientation conditions. Einstein A is younger than Einstein, as indicated by the fact that it lies squarely in the middle of the floor of Einstein. When viewed in topographic data, these two craters reveal much about the relative age and shape of an impact crater. To understand further, let's first take a look at Einstein. Einstein is a fairly large crater that spans 198 km across. A crater's size alone however cannot reveal much about age. ÊEinstein's relative age can be determined by examining the frequency and distribution of impact craters overprinted on its rim and floor. Younger craters have had fewer impacts, which enables them to retain their original morphology. Einstein A reveals most of its original structure, including a raised rim and ejecta blanket, and is therefore a relatively young crater as compared to Einstein, whose original structure has been somewhat degraded over time by smaller impacts. The Einstein craters were named after famed physicist, philosopher, and scientist Albert Einstein (1879-1955). To learn more go to: www.nasa.gov/mission_pages/LRO/multimedia/lroimages/lola-... NASA Goddard Space Flight Center is home to the nation's largest organization of combined scientists, engineers and technologists that build spacecraft, instruments and new technology to study the Earth, the sun, our solar system, and the universe.

Hidden symmetries on Kerr-NUT-(A)dS metrics of Einstein-Sasaki type

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2013-01-01

The hidden symmetries of higher dimensional Euclideanised Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new Killing forms on Einstein-Sasaki manifolds are identified associated with the complex volume form of the cone manifolds. As a concrete example we present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki Y(p, q) spaces. The corresponding hidden symmetries are not anomalous and the geodesic equations are superintegrable.

Bose–Einstein graviton condensate in a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Alfaro, Jorge; Espriu, Domènec; Gabbanelli, Luciano

2018-01-01

We analyze in detail a previous proposal by Dvali and Gómez that black holes could be treated as consisting of a Bose–Einstein condensate of gravitons. In order to do so we extend the Einstein–Hilbert action with a chemical potential-like term, thus placing ourselves in a grand-canonical ensemble. The form and characteristics of this chemical potential-like piece are discussed in some detail. We argue that the resulting equations of motion derived from the action could be interpreted as the Gross–Pitaevskii equation describing a graviton Bose–Einstein condensate trapped by the black hole gravitational field. After this, we proceed to expand the ensuring equations of motion up to second order around the classical Schwarzschild metric so that some non-linear terms in the metric fluctuation are kept. Next we search for solutions and, modulo some very plausible assumptions, we find out that the condensate vanishes outside the horizon but is non-zero in its interior. Inspired by a linearized approximation around the horizon we are able to find an exact solution for the mean-field wave function describing the graviton Bose–Einstein condensate in the black hole interior. After this, we can rederive some of the relations involving the number of gravitons N and the black hole characteristics along the lines suggested by Dvali and Gómez.

How Einstein Discovered E0=mc2

NASA Astrophysics Data System (ADS)

Hecht, Eugene

2012-02-01

This paper traces Einstein's discovery of "the equivalence of mass [m] and energy [E0]." He came to that splendid insight in 1905 while employed by the Bern Patent Office, at which time he was not an especially ardent reader of physics journals. How then did the young savant, working outside of academia in semi-isolation, realize that these two seemingly disparate concepts were actually "identical"? Until now little attention has been given to exploring the physics that guided his thinking in this remarkable endeavor. That work culminated (1907) in the equation E0=mc2, where E0 is "rest energy" and m is "invariant mass." Despite claims to the contrary, Einstein did not write this equation, or its ambiguous variant, E =mc2, in 1905. Furthermore, we will propose a compelling reason for his otherwise inexplicable caution. This paper is meant to help clarify the contemporary literature in the service of an informed pedagogy.

New non-naturally reductive Einstein metrics on exceptional simple Lie groups

NASA Astrophysics Data System (ADS)

Chen, Huibin; Chen, Zhiqi; Deng, Shaoqiang

2018-01-01

In this article, we construct several non-naturally reductive Einstein metrics on exceptional simple Lie groups, which are found through the decomposition arising from generalized Wallach spaces. Using the decomposition corresponding to the two involutions, we calculate the non-zero coefficients in the formulas of the components of Ricci tensor with respect to the given metrics. The Einstein metrics are obtained as solutions of a system of polynomial equations, which we manipulate by symbolic computations using Gröbner bases. In particular, we discuss the concrete numbers of non-naturally reductive Einstein metrics for each case up to isometry and homothety.

Running vacuum cosmological models: linear scalar perturbations

NASA Astrophysics Data System (ADS)

Perico, E. L. D.; Tamayo, D. A.

2017-08-01

In cosmology, phenomenologically motivated expressions for running vacuum are commonly parameterized as linear functions typically denoted by Λ(H2) or Λ(R). Such models assume an equation of state for the vacuum given by bar PΛ = - bar rhoΛ, relating its background pressure bar PΛ with its mean energy density bar rhoΛ ≡ Λ/8πG. This equation of state suggests that the vacuum dynamics is due to an interaction with the matter content of the universe. Most of the approaches studying the observational impact of these models only consider the interaction between the vacuum and the transient dominant matter component of the universe. We extend such models by assuming that the running vacuum is the sum of independent contributions, namely bar rhoΛ = Σibar rhoΛi. Each Λ i vacuum component is associated and interacting with one of the i matter components in both the background and perturbation levels. We derive the evolution equations for the linear scalar vacuum and matter perturbations in those two scenarios, and identify the running vacuum imprints on the cosmic microwave background anisotropies as well as on the matter power spectrum. In the Λ(H2) scenario the vacuum is coupled with every matter component, whereas the Λ(R) description only leads to a coupling between vacuum and non-relativistic matter, producing different effects on the matter power spectrum.

Bose-Einstein correlation within the framework of hadronic mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burande, Chandrakant S.

The Bose-Einstein correlation is the phenomenon in which protons and antiprotons collide at extremely high energies; coalesce one into the other resulting into the fireball of finite dimension. They annihilate each other and produces large number of mesons that remain correlated at distances very large compared to the size of the fireball. It was believed that Einstein’s special relativity and relativistic quantum mechanics are the valid frameworks to represent this phenomenon. Although, these frameworks are incomplete and require arbitrary parameters (chaoticity) to fit the experimental data which are prohibited by the basic axioms of relativistic quantum mechanics, such as thatmore » for the vacuum expectation values. Moreover, correlated mesons can not be treated as a finite set of isolated point-like particles because it is non-local event due to overlapping of wavepackets. Therefore, the Bose-Einstein correlation is incompatible with the axiom of expectation values of quantum mechanics. In contrary, relativistic hadronic mechanics constructed by Santilli allows an exact representation of the experimental data of the Bose-Einstein correlation and restore the validity of the Lorentz and Poincare symmetries under nonlocal and non-Hamiltonian internal effects. Further, F. Cardone and R. Mignani observed that the Bose-Einstein two-point correlation function derived by Santilli is perfectly matched with experimental data at high energy.« less

Soliton resonance in bose-einstein condensate

NASA Technical Reports Server (NTRS)

Zak, Michail; Kulikov, I.

2002-01-01

A new phenomenon in nonlinear dispersive systems, including a Bose-Einstein Condensate (BEC), has been described. It is based upon a resonance between an externally induced soliton and 'eigen-solitons' of the homogeneous cubic Schrodinger equation. There have been shown that a moving source of positive /negative potential induces bright /dark solitons in an attractive / repulsive Bose condensate.

Scalar field coupling to Einstein tensor in regular black hole spacetime

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wu, Chen

2018-02-01

In this paper, we study the perturbation property of a scalar field coupling to Einstein's tensor in the background of the regular black hole spacetimes. Our calculations show that the the coupling constant η imprints in the wave equation of a scalar perturbation. We calculated the quasinormal modes of scalar field coupling to Einstein's tensor in the regular black hole spacetimes by the 3rd order WKB method.

Bose-Einstein condensation of paraxial light

NASA Astrophysics Data System (ADS)

Klaers, J.; Schmitt, J.; Damm, T.; Vewinger, F.; Weitz, M.

2011-10-01

Photons, due to the virtually vanishing photon-photon interaction, constitute to very good approximation an ideal Bose gas, but owing to the vanishing chemical potential a (free) photon gas does not show Bose-Einstein condensation. However, this is not necessarily true for a lower-dimensional photon gas. By means of a fluorescence induced thermalization process in an optical microcavity one can achieve a thermal photon gas with freely adjustable chemical potential. Experimentally, we have observed thermalization and subsequently Bose-Einstein condensation of the photon gas at room temperature. In this paper, we give a detailed description of the experiment, which is based on a dye-filled optical microcavity, acting as a white-wall box for photons. Thermalization is achieved in a photon number-conserving way by photon scattering off the dye molecules, and the cavity mirrors both provide an effective photon mass and a confining potential-key prerequisites for the Bose-Einstein condensation of photons. The experimental results are in good agreement with both a statistical and a simple rate equation model, describing the properties of the thermalized photon gas.

Cosmic vacuum energy decay and creation of cosmic matter.

PubMed

Fahr, Hans-Jörg; Heyl, Michael

2007-09-01

In the more recent literature on cosmological evolutions of the universe, the cosmic vacuum energy has become a nonrenouncable ingredient. The cosmological constant Lambda, first invented by Einstein, but later also rejected by him, presently experiences an astonishing revival. Interestingly enough, it acts like a constant vacuum energy density would also do. Namely, it has an accelerating action on cosmic dynamics, without which, as it appears, presently obtained cosmological data cannot be conciliated with theory. As we are going to show in this review, however, the concept of a constant vacuum energy density is unsatisfactory for very basic reasons because it would claim for a physical reality that acts upon spacetime and matter dynamics without itself being acted upon by spacetime or matter.

Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space

NASA Astrophysics Data System (ADS)

Mišković, Olivera; Olea, Rodrigo

2011-01-01

Motivated by possible applications within the framework of anti-de Sitter gravity/conformal field theory correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D dimensions, and whose electric field is described by nonlinear electrodynamics are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary nonlinear electrodynamic Lagrangian in any dimension D and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedure reproduces the black hole metric in Born-Infeld and conformally invariant electrodynamics previously found in the literature. Altogether, it extends to D>4 the four-dimensional solution obtained by Soleng in logarithmic electrodynamics, which comes from vacuum polarization effects. Falloff conditions for the electromagnetic field that ensure the finiteness of the electric charge are also discussed. The black hole mass and vacuum energy as conserved quantities associated to an asymptotic timelike Killing vector are computed using a background-independent regularization of the gravitational action based on the addition of counterterms which are a given polynomial in the intrinsic and extrinsic curvatures.

Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miskovic, Olivera; Olea, Rodrigo; Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso

2011-01-15

Motivated by possible applications within the framework of anti-de Sitter gravity/conformal field theory correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D dimensions, and whose electric field is described by nonlinear electrodynamics are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary nonlinear electrodynamic Lagrangian in any dimension D and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedure reproduces the black hole metric in Born-Infeld and conformally invariant electrodynamics previously found in the literature. Altogether, itmore » extends to D>4 the four-dimensional solution obtained by Soleng in logarithmic electrodynamics, which comes from vacuum polarization effects. Falloff conditions for the electromagnetic field that ensure the finiteness of the electric charge are also discussed. The black hole mass and vacuum energy as conserved quantities associated to an asymptotic timelike Killing vector are computed using a background-independent regularization of the gravitational action based on the addition of counterterms which are a given polynomial in the intrinsic and extrinsic curvatures.« less

Einstein's osmotic equilibrium of colloidal suspensions in conservative force fields

NASA Astrophysics Data System (ADS)

Fu, Jinxin; Ou-Yang, H. Daniel

2014-09-01

Predicted by Einstein in his 1905 paper on Brownian motion, colloidal particles in suspension reach osmotic equilibrium under gravity. The idea was demonstrated by J.B. Perrin to win Nobel Prize in Physics in 1926. We show Einstein's equation for osmotic equilibrium can be applied to colloids in a conservative force field generated by optical gradient forces. We measure the osmotic equation of state of 100nm Polystyrene latex particles in the presence of KCl salt and PEG polymer. We also obtain the osmotic compressibility, which is important for determining colloidal stability and the internal chemical potential, which is useful for predicting the phase transition of colloidal systems. This generalization allows for the use of any conservative force fields for systems ranging from colloidal systems to macromolecular solutions.

Failure of the Nernst-Einstein equation to correlate electrical resistances and rates of ionic self-exchange across certain fixed charge membranes.

PubMed

Gottlieb, M H; Sollner, K

1968-05-01

The electrical resistances and rates of self-exchange of univalent critical ions across several types of collodion matrix membranes of high ionic selectivity were studied over a wide range of conditions. The relationship which was observed between these quantities with membranes of a certain type, namely those activated with poly-2-vinyl-N-methyl pyridinium bromide, cannot be explained on the basis of current concepts of the movement of ions across ion exchange membranes. Rates of self-exchange across these membranes were several times greater than those calculated from the electrical resistances of the membranes on the basis of an expression derived by the use of the Nernst-Einstein equation. The magnitude of the discrepancy was greatest at low concentrations of the ambient electrolyte solution and was independent of the species of both critical and noncritical ions. The data obtained with other types of collodion matrix membranes were, at least approximately, in agreement with the predictions based on the Nernst-Einstein equation. Self-exchange rates across the anion permeable protamine collodion membranes, and across the cation permeable polystyrene sulfonic acid collodion membranes, were about 20% less than those calculated from the electrical resistances. The direction and magnitude of these differences, also observed by other investigators, are qualitatively understood as an electroosmotic effect. With cation permeable membranes prepared by the oxidation of preformed collodion membranes, almost exact agreement was obtained between measured and calculated self-exchange rates; the cause of the apparent absence of an electroosmotic effect with these membranes is unknown.

Failure of the Nernst-Einstein Equation to Correlate Electrical Resistances and Rates of Ionic Self-Exchange across Certain Fixed Charge Membranes

PubMed Central

Gottlieb, Melvin H.; Sollner, Karl

1968-01-01

The electrical resistances and rates of self-exchange of univalent critical ions across several types of collodion matrix membranes of high ionic selectivity were studied over a wide range of conditions. The relationship which was observed between these quantities with membranes of a certain type, namely those activated with poly-2-vinyl-N-methyl pyridinium bromide, cannot be explained on the basis of current concepts of the movement of ions across ion exchange membranes. Rates of self-exchange across these membranes were several times greater than those calculated from the electrical resistances of the membranes on the basis of an expression derived by the use of the Nernst-Einstein equation. The magnitude of the discrepancy was greatest at low concentrations of the ambient electrolyte solution and was independent of the species of both critical and noncritical ions. The data obtained with other types of collodion matrix membranes were, at least approximately, in agreement with the predictions based on the Nernst-Einstein equation. Self-exchange rates across the anion permeable protamine collodion membranes, and across the cation permeable polystyrene sulfonic acid collodion membranes, were about 20% less than those calculated from the electrical resistances. The direction and magnitude of these differences, also observed by other investigators, are qualitatively understood as an electroosmotic effect. With cation permeable membranes prepared by the oxidation of preformed collodion membranes, almost exact agreement was obtained between measured and calculated self-exchange rates; the cause of the apparent absence of an electroosmotic effect with these membranes is unknown. PMID:5699793

Running vacuum cosmological models: linear scalar perturbations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perico, E.L.D.; Tamayo, D.A., E-mail: elduartep@usp.br, E-mail: tamayo@if.usp.br

In cosmology, phenomenologically motivated expressions for running vacuum are commonly parameterized as linear functions typically denoted by Λ( H {sup 2}) or Λ( R ). Such models assume an equation of state for the vacuum given by P-bar {sub Λ} = - ρ-bar {sub Λ}, relating its background pressure P-bar {sub Λ} with its mean energy density ρ-bar {sub Λ} ≡ Λ/8π G . This equation of state suggests that the vacuum dynamics is due to an interaction with the matter content of the universe. Most of the approaches studying the observational impact of these models only consider the interactionmore » between the vacuum and the transient dominant matter component of the universe. We extend such models by assuming that the running vacuum is the sum of independent contributions, namely ρ-bar {sub Λ} = Σ {sub i} ρ-bar {sub Λ} {sub i} . Each Λ i vacuum component is associated and interacting with one of the i matter components in both the background and perturbation levels. We derive the evolution equations for the linear scalar vacuum and matter perturbations in those two scenarios, and identify the running vacuum imprints on the cosmic microwave background anisotropies as well as on the matter power spectrum. In the Λ( H {sup 2}) scenario the vacuum is coupled with every matter component, whereas the Λ( R ) description only leads to a coupling between vacuum and non-relativistic matter, producing different effects on the matter power spectrum.« less

Gravity and the Spin-2 Planar Schrödinger Equation

NASA Astrophysics Data System (ADS)

Bergshoeff, Eric A.; Rosseel, Jan; Townsend, Paul K.

2018-04-01

A Schrödinger equation proposed for the Girvin-MacDonald-Platzman gapped spin-2 mode of fractional quantum Hall states is found from a novel nonrelativistic limit, applicable only in 2 +1 dimensions, of the massive spin-2 Fierz-Pauli field equations. It is also found from a novel null reduction of the linearized Einstein field equations in 3 +1 dimensions, and in this context a uniform distribution of spin-2 particles implies, via a Brinkmann-wave solution of the nonlinear Einstein equations, a confining harmonic oscillator potential for the individual particles.

Levitating soliton of the Bose–Einstein condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vysotina, N. V.; Rosanov, N. N., E-mail: nnrosanov@mail.ru

We have proposed a mechanical model that corresponds to the Newton equation for describing the dynamics of an oscillon, viz., a soliton-like cluster of the Bose–Einstein condensate (with atomic attraction) placed above an oscillating atomic mirror in a uniform gravitational field. The model describes the stochastic Fermi acceleration and periodic, quasi-periodic, and chaotic motion of the oscillon center, as well as hysteresis phenomena in the case of a slow variation of mirror oscillation frequency, which are in good agreement with the results obtained using the Gross–Pitaevskii equation.

Vacuum energy in Einstein-Gauss-Bonnet anti-de Sitter gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kofinas, Georgios; Olea, Rodrigo

2006-10-15

A finite action principle for Einstein-Gauss-Bonnet anti-de Sitter gravity is achieved by supplementing the bulk Lagrangian by a suitable boundary term, whose form substantially differs in odd and even dimensions. For even dimensions, this term is given by the boundary contribution in the Euler theorem with a coupling constant fixed, demanding the spacetime to have constant (negative) curvature in the asymptotic region. For odd dimensions, the action is stationary under a boundary condition on the variation of the extrinsic curvature. A well-posed variational principle leads to an appropriate definition of energy and other conserved quantities using the Noether theorem, andmore » to a correct description of black hole thermodynamics. In particular, this procedure assigns a nonzero energy to anti-de Sitter spacetime in all odd dimensions.« less

The Einstein Dossiers: Science and Politics - Einstein's Berlin Period with an Appendix on Einstein's FBI File

NASA Astrophysics Data System (ADS)

Grundmann, Siegfried

In 1919 the Prussian Ministry of Science, Arts and Culture opened a dossier on "Einstein's Theory of Relativity." It was rediscovered by the author in 1961 and is used in conjunction with numerous other subsequently identified 'Einstein' files as the basis of this fascinating book. In particular, the author carefully scrutinizes Einstein's FBI file from 1950-55 against mostly unpublished material from European including Soviet sources and presents hitherto unknown documentation on Einstein's alleged contacts with the German Communist Party and the Comintern.

Global existence and large time asymptotic behavior of strong solutions to the Cauchy problem of 2D density-dependent Navier–Stokes equations with vacuum

NASA Astrophysics Data System (ADS)

Lü, Boqiang; Shi, Xiaoding; Zhong, Xin

2018-06-01

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier–Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D Cauchy problem of the density-dependent Navier–Stokes equations on the whole space admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Furthermore, we also obtain the large time decay rates of the spatial gradients of the velocity and the pressure, which are the same as those of the homogeneous case.

Exact example of backreaction of small scale inhomogeneities in cosmology

NASA Astrophysics Data System (ADS)

Green, Stephen; Wald, Robert

2013-04-01

We construct a one-parameter family of polarized vacuum Gowdy spacetimes on a torus. In the limit as the parameter N goes to infinity, the metric uniformly approaches a smooth ``background metric.'' However, spacetime derivatives of the metric do not approach a limit. As a result, we find that the background metric itself is not a solution of the vacuum Einstein equation. Rather, it is a solution of the Einstein equation with an ``effective stress-energy tensor,'' which is traceless and satisfies the weak energy condition. This is an explicit example of backreaction due to small scale inhomogeneities. We comment on the non-vacuum case, where we have proven in previous work that, provided the matter stress-energy tensor satisfies the weak energy condition, no additional backreaction is possible.

BOOK REVIEW: Partial Differential Equations in General Relativity

NASA Astrophysics Data System (ADS)

Halburd, Rodney G.

2008-11-01

Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed

On local strong solutions to the three-dimensional nonhomogeneous incompressible magnetohydrodynamic equations with density-dependent viscosity and vacuum

NASA Astrophysics Data System (ADS)

Song, Sisi

2018-04-01

This paper concerns the three-dimensional nonhomogeneous incompressible magnetohydrodynamic equations with density-dependent viscosity and vacuum on Ω \\subset R^3. The domain Ω \\subset R^3 is a general connected smooth one, either bounded or unbounded. In particular, the initial density can have compact support when Ω is unbounded. First, we obtain the local existence and uniqueness of strong solution to the three-dimensional nonhomogeneous incompressible magnetohydrodynamic equations without any compatibility condition assumed on the initial data. Then, we also prove the continuous dependence of strong solution on the initial data under an additional compatibility condition.

Time symmetry breaking in Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Mendonça, J. T.; Gammal, A.

2017-09-01

We consider different processes leading to time symmetry breaking in a Bose-Einstein condensate. Our approach provides a global description of time symmetry breaking, based on the equations of a thermal condensate. This includes quenching and expansion of the condensate, the Kibble-Zurek mechanism associated with the creation of vorticity, the dynamical Casimir effect and the formation of time crystals.

Inflation in Einstein-Cartan theory with energy-momentum tensor with spin

NASA Technical Reports Server (NTRS)

Fennelly, A. J.; Bradas, James C.; Smalley, Larry L.

1988-01-01

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic (Bianchi Type I) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley (RS) improved energy-momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density.

Radiating black hole solutions in Einstein-Gauss-Bonnet gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dominguez, Alfredo E.; Instituto Universitario Aeronautico, Avenida Fuerza Aerea km 6.5.; Gallo, Emanuel

2006-03-15

In this paper, we find some new exact solutions to the Einstein-Gauss-Bonnet equations. First, we prove a theorem which allows us to find a large family of solutions to the Einstein-Gauss-Bonnet gravity in n-dimensions. This family of solutions represents dynamic black holes and contains, as particular cases, not only the recently found Vaidya-Einstein-Gauss-Bonnet black hole, but also other physical solutions that we think are new, such as the Gauss-Bonnet versions of the Bonnor-Vaidya (de Sitter/anti-de Sitter) solution, a global monopole, and the Husain black holes. We also present a more general version of this theorem in which less restrictive conditionsmore » on the energy-momentum tensor are imposed. As an application of this theorem, we present the exact solution describing a black hole radiating a charged null fluid in a Born-Infeld nonlinear electrodynamics.« less

Gravitational Lensing: Einstein's unfinished symphony

NASA Astrophysics Data System (ADS)

Treu, Tommaso; Ellis, Richard S.

2015-01-01

Gravitational lensing - the deflection of light rays by gravitating matter - has become a major tool in the armoury of the modern cosmologist. Proposed nearly a hundred years ago as a key feature of Einstein's theory of general relativity, we trace the historical development since its verification at a solar eclipse in 1919. Einstein was apparently cautious about its practical utility and the subject lay dormant observationally for nearly 60 years. Nonetheless there has been rapid progress over the past twenty years. The technique allows astronomers to chart the distribution of dark matter on large and small scales thereby testing predictions of the standard cosmological model which assumes dark matter comprises a massive weakly-interacting particle. By measuring the distances and tracing the growth of dark matter structure over cosmic time, gravitational lensing also holds great promise in determining whether the dark energy, postulated to explain the accelerated cosmic expansion, is a vacuum energy density or a failure of general relativity on large scales. We illustrate the wide range of applications which harness the power of gravitational lensing, from searches for the earliest galaxies magnified by massive clusters to those for extrasolar planets which temporarily brighten a background star. We summarise the future prospects with dedicated ground and space-based facilities designed to exploit this remarkable physical phenomenon.

Vacuum fluctuations in an ancestor vacuum: A possible dark energy candidate

NASA Astrophysics Data System (ADS)

Aoki, Hajime; Iso, Satoshi; Lee, Da-Shin; Sekino, Yasuhiro; Yeh, Chen-Pin

2018-02-01

We consider an open universe created by bubble nucleation, and study possible effects of our "ancestor vacuum," a de Sitter space in which bubble nucleation occurred, on the present universe. We compute vacuum expectation values of the energy-momentum tensor for a minimally coupled scalar field, carefully taking into account the effect of the ancestor vacuum by the Euclidean prescription. We pay particular attention to the so-called supercurvature mode, a non-normalizable mode on a spatial slice of the open universe, which has been known to exist for sufficiently light fields. This mode decays in time most slowly, and may leave residual effects of the ancestor vacuum, potentially observable in the present universe. We point out that the vacuum energy of the quantum field can be regarded as dark energy if mass of the field is of order the present Hubble parameter or smaller. We obtain preliminary results for the dark energy equation of state w (z ) as a function of the redshift.

Rogue waves for a discrete (2+1)-dimensional Ablowitz-Ladik equation in the nonlinear optics and Bose-Einstein condensation

NASA Astrophysics Data System (ADS)

Wu, Xiao-Yu; Tian, Bo; Chai, Han-Peng; Du, Zhong

2018-03-01

Under investigation in this paper is a discrete (2+1)-dimensional Ablowitz-Ladik equation, which is used to model the nonlinear waves in the nonlinear optics and Bose-Einstein condensation. Employing the Kadomtsev-Petviashvili hierarchy reduction, we obtain the rogue wave solutions in terms of the Gramian. We graphically study the first-, second- and third-order rogue waves with the influence of the focusing coefficient and coupling strength. When the value of the focusing coefficient increases, both the peak of the rogue wave and background decrease. When the value of the coupling strength increases, the rogue wave raises and decays in a shorter time. High-order rogue waves are exhibited as one single highest peak and some lower humps, and such lower humps are shown as the triangular and circular patterns.

Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

DOE PAGES

Goodman, Roy H.; Kevrekidis, P. G.; Carretero-González, R.

2015-04-14

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ODEs describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. In this study, we uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals inmore » the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system, we are able to construct complex periodic orbits in the original, PDE, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.« less

Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goodman, Roy H.; Kevrekidis, P. G.; Carretero-González, R.

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ODEs describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. In this study, we uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals inmore » the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system, we are able to construct complex periodic orbits in the original, PDE, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.« less

Simple waves in a two-component Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Ivanov, S. K.; Kamchatnov, A. M.

2018-04-01

We study the dynamics of so-called simple waves in a two-component Bose-Einstein condensate. The evolution of the condensate is described by Gross-Pitaevskii equations which can be reduced for these simple wave solutions to a system of ordinary differential equations which coincide with those derived by Ovsyannikov for the two-layer fluid dynamics. We solve the Ovsyannikov system for two typical situations of large and small difference between interspecies and intraspecies nonlinear interaction constants. Our analytic results are confirmed by numerical simulations.

Renormalized vacuum polarization of rotating black holes

NASA Astrophysics Data System (ADS)

Ferreira, Hugo R. C.

2015-04-01

Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS3 black hole solution to topologically massive gravity, a deformation of (2 + 1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization, for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions.

Transcritical flow of a Bose-Einstein condensate through a penetrable barrier

NASA Astrophysics Data System (ADS)

Leszczyszyn, A. M.; El, G. A.; Gladush, Yu. G.; Kamchatnov, A. M.

2009-06-01

The problem of the transcritical flow of a Bose-Einstein condensate through a wide repulsive penetrable barrier is studied analytically using the combination of the locally steady “hydraulic” solution of the one-dimensional Gross-Pitaevskii equation and the solutions of the Whitham modulation equations describing the resolution of the upstream and downstream discontinuities through dispersive shocks. It is shown that within the physically reasonable range of parameters, the downstream dispersive shock is attached to the barrier and effectively represents the train of very slow dark solitons, which can be observed in experiments. The rate of the soliton emission, the amplitudes of the solitons in the train, and the drag force are determined in terms of the Bose-Einstein condensate oncoming flow velocity and the strength of the potential barrier. Good agreement with direct numerical solutions is demonstrated. Connection with recent experiments is discussed.

Horizon structure of rotating Einstein-Born-Infeld black holes and shadow

NASA Astrophysics Data System (ADS)

Atamurotov, Farruh; Ghosh, Sushant G.; Ahmedov, Bobomurat

2016-05-01

We investigate the horizon structure of the rotating Einstein-Born-Infeld solution which goes over to the Einstein-Maxwell's Kerr-Newman solution as the Born-Infeld parameter goes to infinity (β → ∞). We find that for a given β , mass M, and charge Q, there exist a critical spinning parameter aE and rHE, which corresponds to an extremal Einstein-Born-Infeld black hole with degenerate horizons, and aE decreases and rHE increases with increase of the Born-Infeld parameter β , while aEinstein-Born-Infeld black hole with outer and inner horizons. Similarly, the effect of β on the infinite redshift surface and in turn on the ergo-region is also included. It is well known that a black hole can cast a shadow as an optical appearance due to its strong gravitational field. We also investigate the shadow cast by the both static and rotating Einstein-Born-Infeld black hole and demonstrate that the null geodesic equations can be integrated, which allows us to investigate the shadow cast by a black hole which is found to be a dark zone covered by a circle. Interestingly, the shadow of an Einstein-Born-Infeld black hole is slightly smaller than for the Reissner-Nordstrom black hole, which consists of concentric circles, for different values of the Born-Infeld parameter β , whose radius decreases with increase of the value of the parameter β . Finally, we have studied observable distortion parameter for shadow of the rotating Einstein-Born-Infeld black hole.

Einstein and Planck

NASA Astrophysics Data System (ADS)

Heilbron, John

2005-03-01

As an editor of the Annalen der Physik, Max Planck published Einstein's early papers on thermodynamics and on special relativity, which Planck probably was the first major physicist to appreciate. They respected one another not only as physicists but also, for their inspired creation of world pictures, as artists. Planck helped to establish Einstein in a sinecure at the center of German physics, Berlin. Despite their differences in scientific style, social life, politics, and religion, they became fast friends. Their mutual admiration survived World War I, during which Einstein advocated pacifism and Planck signed the infamous Manifesto of the 93 Intellectuals supporting the German invasion of Belgium. It also survived the Weimar Republic, which Einstein favored and Planck disliked. Physics drew them together, as both opposed the Copenhagen Interpretation; so did common decency, as Planck helped to protect Einstein from anti-semitic attacks. Their friendship did not survive the Nazis. As a standing secretary of the Berlin Academy, Planck had to advise Einstein to resign from it before his colleagues, outraged at his criticism of the new Germany from the safety of California, expelled him. Einstein never forgave his old friend and former fellow artist for not protesting publicly against his expulsion and denigration, and other enormities of National Socialism. .

Dark soliton interaction of spinor Bose-Einstein condensates in an optical lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Zaidong; Li Qiuyan

2007-08-15

We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schroedinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision of two solitons is investigated in detail.

Einstein as Evaluator?

ERIC Educational Resources Information Center

Caulley, Darrel N.

1982-01-01

Like any other person, Albert Einstein was an informal evaluator, engaged in placing value on various aspects of his life, work, and the world. Based on Einstein's own statements, this paper speculates about what Einstein would have been like as a connoisseur evaluator, a conceptual evaluator, or a responsive evaluator. (Author/BW)

Stationary Black Holes: Uniqueness and Beyond.

PubMed

Chruściel, Piotr T; Costa, João Lopes; Heusler, Markus

2012-01-01

The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.

Einstein and Millikan

NASA Astrophysics Data System (ADS)

Erwin, Charlotte

2005-03-01

Albert Einstein traveled to America by boat during the great depression to consult with scientists at the California Institute of Technology. He was a theoretical physicist, a Nobel Prize winner, and a 20th century folk hero. Few members of the general public understood his theories, but they idolized him all the same. The invitation came from physicist Robert Millikan, who had initiated a visiting-scholars program at Caltech shortly after he became head of the school in 1921. Einstein's visits to the campus in 1931, 1932, and 1933 capped Millikan's campaign to make Caltech one of the physics capitals of the world. Mount Wilson astronomer Edwin Hubble's discovery that redshifts are proportional to their distances from the observer challenged Einstein's cosmological picture of a static universe. The big question at Caltech in 1931 was whether Einstein would give up his cosmological constant and accept the idea of an expanding universe. By day, Einstein discussed his theory and its interpretation at length with Richard Tolman, Hubble, and the other scientists on the campus. By night, Einstein filled his travel diary with his personal impressions. During his third visit, Einstein sidestepped as long as possible the question of whether conditions in Germany might prevent his return there. After the January 30 announcement that Hitler had become chancellor of Germany, the question could no longer be evaded. He postponed his return trip for a few weeks and then went to Belgium for several months instead of to Berlin. In the fall of 1933, Albert Einstein returned to the United States as an emigre and became a charter member of Abraham Flexner's new Institute for Advanced Study in Princeton, New Jersey. Why did Einstein go to Princeton and not Pasadena?

The Happiest thought of Einstein's Life

NASA Astrophysics Data System (ADS)

Heller, Michael

Finally, let us have a closer look at the place of the equivalence principle in the logical scheme of Einstein's general relativity theory. First, Einstein new well, from Minkowski's geometric formulation of his own special relativity, that accelerated motions should be represented as curved lines in a flat space-time. Second, the Galileo principle asserts that all bodies are accelerated in the same way in a given gravitational field, and consequently their motions are represented in the flat space-time by curved lines, all exactly in the same way. Third, since all lines representing free motions are curved exactly in the same way in the flat space-time, one can say that the lines remain straight (as far as possible) but the space-time itself becomes curved. Fourth, and last, since acceleration is (locally) equivalent to a gravitational field (here we have the equivalence principle), one is entitled to assert that it is the gravitational field (and not acceleration) that is represented as the curvature of space-time. This looks almost like an Aristotelian syllogism. However, to put all the pieces of evidence into the logical chain took Einstein a few years of hard thinking. The result has been incorporated into the field equations which quantitatively show how the curvature of space-time and gravity are linked together.

Generalized Einstein relation for the mutual diffusion coefficient of a binary fluid mixture.

PubMed

Felderhof, B U

2017-08-21

The method employed by Einstein to derive his famous relation between the diffusion coefficient and the friction coefficient of a Brownian particle is used to derive a generalized Einstein relation for the mutual diffusion coefficient of a binary fluid mixture. The expression is compared with the one derived by de Groot and Mazur from irreversible thermodynamics and later by Batchelor for a Brownian suspension. A different result was derived by several other workers in irreversible thermodynamics. For a nearly incompressible solution, the generalized Einstein relation agrees with the expression derived by de Groot and Mazur. The two expressions also agree to first order in solute density. For a Brownian suspension, the result derived from the generalized Smoluchowski equation agrees with both expressions.

An Out-of-Math Experience: Einstein, Relativity, and the Developmental Mathematics Student.

ERIC Educational Resources Information Center

Fiore, Greg

2000-01-01

Discusses Einstein's special relativity theory and some of the developmental mathematics involved. Presents motivational classroom materials used in discussing relative-motion problems, evaluating a radical expression, graphing with asymptotes, interpreting a graph, studying variation, and solving literal and radical equations. (KHR)

Exact solutions for coupled Einstein, Dirac, Maxwell, and zero-mass scalar fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patra, A.C.; Ray, D.

1987-12-01

Coupled equations for Einstein, Maxwell, Dirac, and zero-mass scalar fields studied by Krori, Bhattacharya, and Nandi are integrated for plane-symmetric time-independent case. It is shown that solutions do not exist for the plane-symmetric time-dependent case.

Solitons in Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Carr, Lincoln D.

2003-05-01

The stationary form, dynamical properties, and experimental criteria for creation of matter-wave bright and dark solitons, both singly and in trains, are studied numerically and analytically in the context of Bose-Einstein condensates [1]. The full set of stationary solutions in closed analytic form to the mean field model in the quasi-one-dimensional regime, which is a nonlinear Schrodinger equation equally relevant in nonlinear optics, is developed under periodic and box boundary conditions [2]. These solutions are extended numerically into the two and three dimensional regimes, where it is shown that dark solitons can be used to create vortex-anti-vortex pairs under realistic conditions. Specific experimental prescriptions for creating viable dark and bright solitons in the quasi-one-dimensional regime are provided. These analytic methods are then extended to treat the nonlinear Schrodinger equation with a generalized lattice potential, which models a Bose-Einstein condensate trapped in the potential generated by a standing light wave. A novel solution family is developed and stability criterion are presented. Experiments which successfully carried out these ideas are briefly discussed [3]. [1] Dissertation research completed at the University of Washington Physics Department under the advisorship of Prof. William P. Reinhardt. [2] L. D. Carr, C. W. Clark, and W. P. Reinhardt, Phys. Rev. A v. 62 p. 063610-1--10 and Phys. Rev. A v.62, p.063611-1--10 (2000). [3] L. Khaykovich, F. Schreck, T. Bourdel, J. Cubizolles, G. Ferrari, L. D. Carr, Y. Castin, and C. Salomon, Science v. 296, p.1290--1293 (2002).

Perfect fluids in the Einstein-Cartan theory

NASA Technical Reports Server (NTRS)

Ray, J. R.; Smalley, L. J.

1982-01-01

It is pointed out that whereas most of the discussion of the Einstein-Cartan (EC) theory involves the relationship between gravitation and elementary particles, it is possible that the theory, if correct, may be important in certain extreme astrophysical and cosmological problems. The latter would include something like the collapse of a spinning star or an early universe with spin. A set of equations that describe a macroscopic perfect fluid in the EC theory is derived and examined. The equations are derived starting from the fundamental variational principle for a perfect fluid in general relativity. A brief review of the study by Ray (1972) is included, and the results for the EC theory are presented.

Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cadoni, Mariano; Serra, Matteo; Mignemi, Salvatore

We propose a general method for solving exactly the static field equations of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field. Our method starts from an ansatz for the scalar field profile, and determines, together with the metric functions, the corresponding form of the scalar self-interaction potential. Using this method we prove a new no-hair theorem about the existence of hairy black-hole and black-brane solutions and derive broad classes of static solutions with radial symmetry of the theory, which may play an important role in applications of the AdS/CFT correspondence to condensed matter and strongly coupled QFTs. Thesemore » solutions include: (1) four- or generic (d+2)-dimensional solutions with planar, spherical or hyperbolic horizon topology; (2) solutions with anti-de Sitter, domain wall and Lifshitz asymptotics; (3) solutions interpolating between an anti-de Sitter spacetime in the asymptotic region and a domain wall or conformal Lifshitz spacetime in the near-horizon region.« less

Stability of the Einstein static universe in Einstein-Cartan theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Atazadeh, K., E-mail: atazadeh@azaruniv.ac.ir

The existence and stability of the Einstein static solution have been built in the Einstein-Cartan gravity. We show that this solution in the presence of perfect fluid with spin density satisfying the Weyssenhoff restriction is cyclically stable around a center equilibrium point. Thus, study of this solution is interesting because it supports non-singular emergent cosmological models in which the early universe oscillates indeterminately about an initial Einstein static solution and is thus past eternal.

Bright-type and dark-type vector solitons of the (2 + 1)-dimensional spatially modulated quintic nonlinear Schrödinger equation in nonlinear optics and Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Wu, Hong-Yu; Jiang, Li-Hong

2018-03-01

We study a (2 + 1) -dimensional N -coupled quintic nonlinear Schrödinger equation with spatially modulated nonlinearity and transverse modulation in nonlinear optics and Bose-Einstein condensate, and obtain bright-type and dark-type vector multipole as well as vortex soliton solutions. When the modulation depth q is fixed as 0 and 1, we can construct vector multipole and vortex solitons, respectively. Based on these solutions, we investigate the form and phase characteristics of vector multipole and vortex solitons.

Centenarian Einstein

DOE Office of Scientific and Technical Information (OSTI.GOV)

None

2006-05-02

Commemoration of Albert Einstein with 4 speakers to honor his memory: Professor Weisskopf speaks about the scientifically engaged man. Daniel Amati speaks about the climate of the domain of physics during the 1920s, and Sergio Fubini speaks about the scientific hour of Einstein and Berob.

Centenarian Einstein

ScienceCinema

None

2018-05-18

Commemoration of Albert Einstein with 4 speakers to honor his memory: Professor Weisskopf speaks about the scientifically engaged man. Daniel Amati speaks about the climate of the domain of physics during the 1920s, and Sergio Fubini speaks about the scientific hour of Einstein and Berob.

Celebrating Einstein

NASA Astrophysics Data System (ADS)

Key, Joey; Yunes, Nicolas

2013-04-01

The Gravity Group at Montana State University (MSU) hosted Celebrating Einstein, a free public arts and multimedia event celebrating Einstein and his ideas in Bozeman, Montana April 2-6, 2013. The products of our efforts are now available to any party interested in hosting a similar event. Celebrating Einstein is a truly interdisciplinary effort including art, film, dance, music, physics, history, and education. Events included a black hole immersive art installation, a series of public talks by physicists, and Einstein lessons in the public schools leading up to a live free public multimedia performance including a professional dance company, a live interview with a renowned physicist, and an original score composed for the MSU student symphony to be performed with an original film produced by the Science and Natural History film program at MSU. This project is funded by the Montana Space Grant Consortium, Montana State University, and the National Science Foundation.

Bose-Einstein condensates in charged black-hole spacetimes

NASA Astrophysics Data System (ADS)

Castellanos, Elías; Degollado, Juan Carlos; Lämmerzahl, Claus; Macías, Alfredo; Perlick, Volker

2018-01-01

We analyze Bose-Einstein condensates on three types of spherically symmetric and static charged black-hole spacetimes: the Reissner-Nordström spacetime, Hoffmann's Born-Infeld black-hole spacetime, and the regular Ayón-Beato-García spacetime. The Bose-Einstein condensate is modeled in terms of a massive scalar field that satisfies a Klein-Gordon equation with a self-interaction term. The scalar field is assumed to be uncharged and not self-gravitating. If the mass parameter of the scalar field is chosen sufficiently small, there are quasi-bound states of the scalar field that may be interpreted as dark matter clouds. We estimate the size and the total energy of such clouds around charged supermassive black holes and we investigate if their observable features can be used for discriminating between the different types of charged black holes.

Hypergeometric Equation in Modeling Relativistic Isotropic Sphere

NASA Astrophysics Data System (ADS)

Thirukkanesh, S.; Ragel, F. C.

2014-04-01

We study the Einstein system of equations in static spherically symmetric spacetimes. We obtained classes of exact solutions to the Einstein system by transforming the condition for pressure isotropy to a hypergeometric equation choosing a rational form for one of the gravitational potentials. The solutions are given in simple form that is a desirable requisite to study the behavior of relativistic compact objects in detail. A physical analysis indicate that our models satisfy all the fundamental requirements of realistic star and match smoothly with the exterior Schwarzschild metric. The derived masses and densities are consistent with the previously reported experimental and theoretical studies describing strange stars. The models satisfy the standard energy conditions required by normal matter.

Shock Waves in a Bose-Einstein Condensate

NASA Technical Reports Server (NTRS)

Kulikov, Igor; Zak, Michail

2005-01-01

A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.

Spacetimes with Killing tensors. [for Einstein-Maxwell fields with certain spinor indices

NASA Technical Reports Server (NTRS)

Hughston, L. P.; Sommers, P.

1973-01-01

The characteristics of the Killing equation and the Killing tensor are discussed. A conformal Killing tensor is of interest inasmuch as it gives rise to a quadratic first integral for null geodesic orbits. The Einstein-Maxwell equations are considered together with the Bianchi identity and the conformal Killing tensor. Two examples for the application of the considered relations are presented, giving attention to the charged Kerr solution and the charged C-metric.

Hidden symmetries in Sasaki-Einstein geometries

NASA Astrophysics Data System (ADS)

Slesar, V.; Visinescu, M.; Vîlcu, G. E.

2017-07-01

We describe a method for constructing Killing-Yano tensors on Sasaki spaces using their geometrical properties, without the need of solving intricate generalized Killing equations. We obtain the Killing-Yano tensors on toric Sasaki-Einstein spaces using the fact that the metric cones of these spaces are Calabi-Yau manifolds which in turn are described in terms of toric data. We extend the search of Killing-Yano tensors on mixed 3-Sasakian manifolds. We illustrate the method by explicit construction of Killing forms on some spaces of current interest.

Integrability of geodesics and action-angle variables in Sasaki-Einstein space T^{1,1}

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2016-09-01

We briefly describe the construction of Stäkel-Killing and Killing-Yano tensors on toric Sasaki-Einstein manifolds without working out intricate generalized Killing equations. The integrals of geodesic motions are expressed in terms of Killing vectors and Killing-Yano tensors of the homogeneous Sasaki-Einstein space T^{1,1}. We discuss the integrability of geodesics and construct explicitly the action-angle variables. Two pairs of frequencies of the geodesic motions are resonant giving way to chaotic behavior when the system is perturbed.

BOOK REVIEW: Einstein's General Theory of Relativity—with Modern Applications in Cosmology

NASA Astrophysics Data System (ADS)

Barrabès, C.

2008-09-01

forms and on vectors (exterior covariant and Lie derivatives) are presented, and emphasis is given to the Cartan formalism as it is later systematically used to derive the curvature tensor and for solutions of the Einstein field equations. One also finds the properties of hypersurfaces, such as the intrinsic and extrinsic curvatures and the Gauss Codazzi relations. This makes this part of the book very useful and convenient since those important elements are gathered in one place. However the density of exposition in this part might appear a bit steep to a reader without some previous knowledge of differential geometry. Part III deals with Einstein's field equations, and their applications to gravitational waves and black holes. The field equations are derived from a variational principle, the geometrical part (Einstein tensor) from the Einstein Hilbert action, and the matter part (stress energy tensor) from a generic action integral for matter. Various examples of stress energy tensors and in particular, for fluids, are considered, and several are used later in cosmology (for instance quintessence and Lorentz invariant vacuum energy). A short chapter on the linear approximation and gravitational waves then follows and it is good to see a section on gravito-electromagnetism. This part ends with a chapter devoted to black holes which is perhaps the weakest part of the book as it is quite sketchy. However this is to be expected in a book with an emphasis on cosmology, and such topics are extensively described in other books. The rest of the book (parts IV and V) is essentially concerned with cosmology. The authors give a detailed description of the applications of the Einstein field equations to a universe with various matter contents, and present in a successful way the recent developments in this domain. The first chapter of part IV describes the standard homogeneous and isotropic cosmological model. It is followed by an interesting chapter dealing with universes

Higher-order stochastic differential equations and the positive Wigner function

NASA Astrophysics Data System (ADS)

Drummond, P. D.

2017-12-01

General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.

Gravitational waves in Einstein-æther and generalized TeVeS theory after GW170817

NASA Astrophysics Data System (ADS)

Gong, Yungui; Hou, Shaoqi; Liang, Dicong; Papantonopoulos, Eleftherios

2018-04-01

In this work we discuss the polarization contents of Einstein-æther theory and the generalized tensor-vector-scalar (TeVeS) theory, as both theories have a normalized timelike vector field. We derive the linearized equations of motion around the flat spacetime background using the gauge-invariant variables to easily separate physical degrees of freedom. We find the plane wave solutions and identify the polarizations by examining the geodesic deviation equations. We find that there are five polarizations in Einstein-æther theory and six polarizations in the generalized TeVeS theory. In particular, the transverse breathing mode is mixed with the pure longitudinal mode. We also discuss the experimental tests of the extra polarizations in Einstein-æther theory using pulsar timing arrays combined with the gravitational-wave speed bound derived from the observations on GW 170817 and GRB 170817A. It turns out that it might be difficult to use pulsar timing arrays to distinguish different polarizations in Einstein-æther theory. The same speed bound also forces one of the propagating modes in the generalized TeVeS theory to travel much faster than the speed of light. Since the strong coupling problem does not exist in some parameter subspaces, the generalized TeVeS theory is excluded in these parameter subspaces.

Bose-Einstein condensation of dark matter axions.

PubMed

Sikivie, P; Yang, Q

2009-09-11

We show that cold dark matter axions thermalize and form a Bose-Einstein condensate (BEC). We obtain the axion state in a homogeneous and isotropic universe, and derive the equations governing small axion perturbations. Because they form a BEC, axions differ from ordinary cold dark matter in the nonlinear regime of structure formation and upon entering the horizon. Axion BEC provides a mechanism for the production of net overall rotation in dark matter halos, and for the alignment of cosmic microwave anisotropy multipoles.

Stationary Black Holes: Uniqueness and Beyond.

PubMed

Heusler, Markus

1998-01-01

The spectrum of known black hole solutions to the stationary Einstein equations has increased in an unexpected way during the last decade. In particular, it has turned out that not all black hole equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black hole space-times ceases to exist in self-gravitating non-linear field theories. This text aims to review some of the recent developments and to discuss them in the light of the uniqueness theorem for the Einstein-Maxwell system.

Dynamic wormhole solutions in Einstein-Cartan gravity

NASA Astrophysics Data System (ADS)

Mehdizadeh, Mohammad Reza; Ziaie, Amir Hadi

2017-12-01

In the present work, we investigate evolving wormhole configurations described by a constant redshift function in Einstein-Cartan theory. The matter content consists of a Weyssenhoff fluid along with an anisotropic matter which together generalize the anisotropic energy momentum tensor in general relativity in order to include the effects of intrinsic angular momentum (spin) of particles. Using a generalized Friedmann-Robertson-Walker spacetime, we derive analytical evolving wormhole geometries by assuming a particular equation of state for energy density and pressure profiles. We introduce exact asymptotically flat and anti-de Sitter spacetimes that admit traversable wormholes and respect energy conditions throughout the spacetime. The rate of expansion of these evolving wormholes is determined only by the Friedmann equation in the presence of spin effects.

Stability and Instability of the Sub-extremal Reissner-Nordström Black Hole Interior for the Einstein-Maxwell-Klein-Gordon Equations in Spherical Symmetry

NASA Astrophysics Data System (ADS)

Van de Moortel, Maxime

2018-05-01

We show non-linear stability and instability results in spherical symmetry for the interior of a charged black hole—approaching a sub-extremal Reissner-Nordström background fast enough—in presence of a massive and charged scalar field, motivated by the strong cosmic censorship conjecture in that setting: 1. Stability We prove that spherically symmetric characteristic initial data to the Einstein-Maxwell-Klein-Gordon equations approaching a Reissner-Nordström background with a sufficiently decaying polynomial decay rate on the event horizon gives rise to a space-time possessing a Cauchy horizon in a neighbourhood of time-like infinity. Moreover, if the decay is even stronger, we prove that the space-time metric admits a continuous extension to the Cauchy horizon. This generalizes the celebrated stability result of Dafermos for Einstein-Maxwell-real-scalar-field in spherical symmetry. 2. Instability We prove that for the class of space-times considered in the stability part, whose scalar field in addition obeys a polynomial averaged- L 2 (consistent) lower bound on the event horizon, the scalar field obeys an integrated lower bound transversally to the Cauchy horizon. As a consequence we prove that the non-degenerate energy is infinite on any null surface crossing the Cauchy horizon and the curvature of a geodesic vector field blows up at the Cauchy horizon near time-like infinity. This generalizes an instability result due to Luk and Oh for Einstein-Maxwell-real-scalar-field in spherical symmetry. This instability of the black hole interior can also be viewed as a step towards the resolution of the C 2 strong cosmic censorship conjecture for one-ended asymptotically flat initial data.

Entropy density of an adiabatic relativistic Bose-Einstein condensate star

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khaidir, Ahmad Firdaus; Kassim, Hasan Abu; Yusof, Norhasliza

Inspired by recent works, we investigate how the thermodynamics parameters (entropy, temperature, number density, energy density, etc) of Bose-Einstein Condensate star scale with the structure of the star. Below the critical temperature in which the condensation starts to occur, we study how the entropy behaves with varying temperature till it reaches its own stability against gravitational collapse and singularity. Compared to photon gases (pressure is described by radiation) where the chemical potential, μ is zero, entropy of photon gases obeys the Stefan-Boltzmann Law for a small values of T while forming a spiral structure for a large values of Tmore » due to general relativity. The entropy density of Bose-Einstein Condensate is obtained following the similar sequence but limited under critical temperature condition. We adopt the scalar field equation of state in Thomas-Fermi limit to study the characteristics of relativistic Bose-Einstein condensate under varying temperature and entropy. Finally, we obtain the entropy density proportional to (σT{sup 3}-3T) which obeys the Stefan-Boltzmann Law in ultra-relativistic condition.« less

Subsonic and Supersonic Effects in Bose-Einstein Condensate

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

A paper presents a theoretical investigation of subsonic and supersonic effects in a Bose-Einstein condensate (BEC). The BEC is represented by a time-dependent, nonlinear Schroedinger equation that includes terms for an external confining potential term and a weak interatomic repulsive potential proportional to the number density of atoms. From this model are derived Madelung equations, which relate the quantum phase with the number density, and which are used to represent excitations propagating through the BEC. These equations are shown to be analogous to the classical equations of flow of an inviscid, compressible fluid characterized by a speed of sound (g/Po)1/2, where g is the coefficient of the repulsive potential and Po is the unperturbed mass density of the BEC. The equations are used to study the effects of a region of perturbation moving through the BEC. The excitations created by a perturbation moving at subsonic speed are found to be described by a Laplace equation and to propagate at infinite speed. For a supersonically moving perturbation, the excitations are found to be described by a wave equation and to propagate at finite speed inside a Mach cone.

Charged anisotropic matter with linear or nonlinear equation of state

NASA Astrophysics Data System (ADS)

Varela, Victor; Rahaman, Farook; Ray, Saibal; Chakraborty, Koushik; Kalam, Mehedi

2010-08-01

Ivanov pointed out substantial analytical difficulties associated with self-gravitating, static, isotropic fluid spheres when pressure explicitly depends on matter density. Simplifications achieved with the introduction of electric charge were noticed as well. We deal with self-gravitating, charged, anisotropic fluids and get even more flexibility in solving the Einstein-Maxwell equations. In order to discuss analytical solutions we extend Krori and Barua’s method to include pressure anisotropy and linear or nonlinear equations of state. The field equations are reduced to a system of three algebraic equations for the anisotropic pressures as well as matter and electrostatic energy densities. Attention is paid to compact sources characterized by positive matter density and positive radial pressure. Arising solutions satisfy the energy conditions of general relativity. Spheres with vanishing net charge contain fluid elements with unbounded proper charge density located at the fluid-vacuum interface. Notably the electric force acting on these fluid elements is finite, although the acting electric field is zero. Net charges can be huge (1019C) and maximum electric field intensities are very large (1023-1024statvolt/cm) even in the case of zero net charge. Inward-directed fluid forces caused by pressure anisotropy may allow equilibrium configurations with larger net charges and electric field intensities than those found in studies of charged isotropic fluids. Links of these results with charged strange quark stars as well as models of dark matter including massive charged particles are highlighted. The van der Waals equation of state leading to matter densities constrained by cubic polynomial equations is briefly considered. The fundamental question of stability is left open.

Investigation of Bose-Einstein Condensates in q-Deformed Potentials with First Order Perturbation Theory

NASA Astrophysics Data System (ADS)

Nutku, Ferhat; Aydıner, Ekrem

2018-02-01

The Gross-Pitaevskii equation, which is the governor equation of Bose-Einstein condensates, is solved by first order perturbation expansion under various q-deformed potentials. Stationary probability distributions reveal one and two soliton behavior depending on the type of the q-deformed potential. Additionally a spatial shift of the probability distribution is found for the dark soliton solution, when the q parameter is changed.

Static Einstein-Maxwell Black Holes with No Spatial Isometries in AdS Space.

PubMed

Herdeiro, Carlos A R; Radu, Eugen

2016-11-25

We explicitly construct static black hole solutions to the fully nonlinear, D=4, Einstein-Maxwell-anti-de Sitter (AdS) equations that have no continuous spatial symmetries. These black holes have a smooth, topologically spherical horizon (section), but without isometries, and approach, asymptotically, global AdS spacetime. They are interpreted as bound states of a horizon with the Einstein-Maxwell-AdS solitons recently discovered, for appropriate boundary data. In sharp contrast to the uniqueness results for a Minkowski electrovacuum, the existence of these black holes shows that single, equilibrium, black hole solutions in an AdS electrovacuum admit an arbitrary multipole structure.

Equivalent equations of motion for gravity and entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space and fields on this space. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

Equivalent equations of motion for gravity and entropy

DOE PAGES

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; ...

2017-02-01

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space and fields on this space. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

Chapter 5. Hidden Symmetry and Exact Solutions in Einstein Gravity

NASA Astrophysics Data System (ADS)

Yasui, Y.; Houri, T.

Conformal Killing-Yano tensors are introduced as ageneralization of Killing vectors. They describe symmetries of higher-dimensional rotating black holes. In particular, a rank-2 closed conformal Killing-Yano tensor generates the tower of both hidden symmetries and isometries. We review a classification of higher-dimensional spacetimes admitting such a tensor, and present exact solutions to the Einstein equations for these spacetimes.

Bohr's Electron was Problematic for Einstein: String Theory Solved the Problem

NASA Astrophysics Data System (ADS)

Webb, William

2013-04-01

Neils Bohr's 1913 model of the hydrogen electron was problematic for Albert Einstein. Bohr's electron rotates with positive kinetic energies +K but has addition negative potential energies - 2K. The total net energy is thus always negative with value - K. Einstein's special relativity requires energies to be positive. There's a Bohr negative energy conflict with Einstein's positive energy requirement. The two men debated the problem. Both would have preferred a different electron model having only positive energies. Bohr and Einstein couldn't find such a model. But Murray Gell-Mann did! In the 1960's, Gell-Mann introduced his loop-shaped string-like electron. Now, analysis with string theory shows that the hydrogen electron is a loop of string-like material with a length equal to the circumference of the circular orbit it occupies. It rotates like a lariat around its centered proton. This loop-shape has no negative potential energies: only positive +K relativistic kinetic energies. Waves induced on loop-shaped electrons propagate their energy at a speed matching the tangential speed of rotation. With matching wave speed and only positive kinetic energies, this loop-shaped electron model is uniquely suited to be governed by the Einstein relativistic equation for total mass-energy. Its calculated photon emissions are all in excellent agreement with experimental data and, of course, in agreement with those -K calculations by Neils Bohr 100 years ago. Problem solved!

Einstein Meets Hilbert: At the Crossroads of Physics and Mathematics

NASA Astrophysics Data System (ADS)

Rowe, David E.

One of the most famous episodes in the early history of general relativity involves the ``race'' in November 1915 between Albert Einstein and David Hilbert to uncover the ``correct'' form for the ten gravitational field equations. In light of recent archival findings, however, this story now has become a topic of renewed interest and controversy among historians of physics and mathematics. Drawing on recent studies and newly found sources, the present essay takes up this familiar tale from a new perspective, one that has seldom received due attention in the standard literature, namely, the mathematical issues at the heart of Einstein's theory. Told from this angle, the leading actors are Einstein's collaborator Marcel Grossmann, his critic Tullio Levi-Civita, his competitor David Hilbert, and several other mathematicians, many of them connected with Hilbert's Göttingen colleagues such as Hermann Weyl, Felix Klein, and Emmy Noether. As Einstein was the first to admit, Göttingen was far more important than Berlin as an active center for research in general relativity. Any account which, like this one, tries to understand both the actions and motives of the leading players must confront the problem of interpreting the rather sparse documentary evidence available. The interpretation offered herein, whatever its merits, aims first and foremost to show how mathematical issues deeply permeated the early history of general relativity.

Double-slit interferometry with a Bose-Einstein condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Collins, L.A.; Berman, G.P.; Bishop, A.R.

2005-03-01

A Bose-Einstein 'double-slit' interferometer has been recently realized experimentally by Y. Shin et al., Phys. Rev. Lett. 92 050405 (2004). We analyze the interferometric steps by solving numerically the time-dependent Gross-Pitaevskii equation in three-dimensional space. We focus on the adiabaticity time scales of the problem and on the creation of spurious collective excitations as a possible source of the strong degradation of the interference pattern observed experimentally. The role of quantum fluctuations is discussed.

Compactified Vacuum in Ten Dimensions.

NASA Astrophysics Data System (ADS)

Wurmser, Daniel

1987-09-01

Since the 1920's, theories which unify gravity with the other fundamental forces have called for more than the four observed dimensions of space-time. According to such a theory, the vacuum consists of flat four-dimensional space-time described by the Minkowski metric M ^4 and a "compactified" space B. The dimensions of B are small, and the space can only be observed at distance scales smaller than the present experimental limit. These theories have had serious difficulties. The equations of gravity severely restrict the possible choices for the space B. The allowed spaces are complicated and difficult to study. The vacuum is furthermore unstable in the sense that a small perturbation causes the compactified dimensions to expand indefinitely. There is an addition a semi-classical argument which implies that the compactified vacuum be annihilated by virtual black holes. It follows that a universe with compactified extra dimensions could not have survived to the present. These results were derived by applying the equations of general relativity to spaces of more than four dimensions. The form of these equations was assumed to be unchanged by an increase in the number of dimensions. Recently, it has been proposed that gravity in more than four dimensions may involve terms of higher order in the curvature as well as the linear terms present in ordinary general relativity. I illustrate the effect of such terms by considering the example B = S^6 where S ^6 is the six-dimensional sphere. Only when the extra terms are included is this choice of the compactified space allowed. I explore the effect of a small perturbation on such a vacuum. The ten-dimensional spherically symmetric potential is examined, and I determine conditions under which the formation of virtual black holes is forbidden. The example M^4 times S^6 is still plagued by the semi -classical instability, but this result does not hold in general. The requirement that virtual black holes be forbidden provides a

Killing Forms on the Five-Dimensional Einstein-Sasaki Y(p, q) Spaces

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2012-12-01

We present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki Y(p, q) spaces. Two new Killing-Yano tensors are identified, associated with the complex volume form of the Calabi-Yau metric cone. The corresponding hidden symmetries are not anomalous and the geodesic equations are superintegrable.

Multisymplectic unified formalism for Einstein-Hilbert gravity

NASA Astrophysics Data System (ADS)

Gaset, Jordi; Román-Roy, Narciso

2018-03-01

We present a covariant multisymplectic formulation for the Einstein-Hilbert model of general relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified Lagrangian-Hamiltonian formalism is particularly interesting when it is applied to these kinds of theories, since it simplifies the treatment of them, in particular, the implementation of the constraint algorithm, the retrieval of the Lagrangian description, and the construction of the covariant Hamiltonian formalism. In order to apply this algorithm to the covariant field equations, they must be written in a suitable geometrical way, which consists of using integrable distributions, represented by multivector fields of a certain type. We apply all these tools to the Einstein-Hilbert model without and with energy-matter sources. We obtain and explain the geometrical and physical meaning of the Lagrangian constraints and we construct the multimomentum (covariant) Hamiltonian formalisms in both cases. As a consequence of the gauge freedom and the constraint algorithm, we see how this model is equivalent to a first-order regular theory, without gauge freedom. In the case of the presence of energy-matter sources, we show how some relevant geometrical and physical characteristics of the theory depend on the type of source. In all the cases, we obtain explicitly multivector fields which are solutions to the gravitational field equations. Finally, a brief study of symmetries and conservation laws is done in this context.

Rediscovering Einstein's legacy: How Einstein anticipates Kuhn and Feyerabend on the nature of science.

PubMed

Oberheim, Eric

2016-06-01

Thomas Kuhn and Paul Feyerabend promote incommensurability as a central component of their conflicting accounts of the nature of science. This paper argues that in so doing, they both develop Albert Einstein's views, albeit in different directions. Einstein describes scientific revolutions as conceptual replacements, not mere revisions, endorsing 'Kant-on-wheels' metaphysics in light of 'world change'. Einstein emphasizes underdetermination of theory by evidence, rational disagreement in theory choice, and the non-neutrality of empirical evidence. Einstein even uses the term 'incommensurable' specifically to apply to challenges posed to comparatively evaluating scientific theories in 1949, more than a decade before Kuhn and Feyerabend. This analysis shows how Einstein anticipates substantial components of Kuhn and Feyerabend's views, and suggests that there are strong reasons to suspect that Kuhn and Feyerabend were directly inspired by Einstein's use of the term 'incommensurable', as well as his more general methodological and philosophical reflections. Copyright © 2015 Elsevier Ltd. All rights reserved.

A Programmable Cellular-Automata Polarized Dirac Vacuum

NASA Astrophysics Data System (ADS)

Osoroma, Drahcir S.

2013-09-01

We explore properties of a `Least Cosmological Unit' (LCU) as an inherent spacetime raster tiling or tessellating the unique backcloth of Holographic Anthropic Multiverse (HAM) cosmology as an array of programmable cellular automata. The HAM vacuum is a scale-invariant HD extension of a covariant polarized Dirac vacuum with `bumps' and `holes' typically described by extended electromagnetic theory corresponding to an Einstein energy-dependent spacetime metric admitting a periodic photon mass. The new cosmology incorporates a unique form of M-Theoretic Calabi-Yau-Poincaré Dodecadedral-AdS5-DS5space (PDS) with mirror symmetry best described by an HD extension of Cramer's Transactional Interpretation when integrated also with an HD extension of the de Broglie-Bohm-Vigier causal interpretation of quantum theory. We incorporate a unique form of large-scale additional dimensionality (LSXD) bearing some similarity to that conceived by Randall and Sundrum; and extend the fundamental basis of our model to the Unified Field, UF. A Sagnac Effect rf-pulsed incursive resonance hierarchy is utilized to manipulate and ballistically program the geometric-topological properties of this putative LSXD space-spacetime network. The model is empirically testable; and it is proposed that a variety of new technologies will arise from ballistic programming of tessellated LCU vacuum cellular automata.

[Never forget this in making your drawings and equations! A conversation with Albert Einstein on learning, teaching and the secrets of the world].

PubMed

Brunner, A

2009-03-01

Albert Einstein, the genius--this aspect often has been noted. A neglected aspect is Einstein's role as student and teacher. For this reason, Einstein's notes have been looked at once again. The selected original quotes are composed into the format of a fictive dialogue. The original context and coherence of his comments have thereby been respected carefully.

Einstein's Jury: Trial by Telescope

NASA Astrophysics Data System (ADS)

Crelinsten, Jeffrey

2007-03-01

While Einstein's theory of relativity ultimately laid the foundation for modern studies of the universe, it took a long time to be accepted. Between 1905 and 1930, relativity was poorly understood and Einstein worked hard to try to make it more accessible to scientists and scientifically literate laypeople. Its acceptance was largely due to the astronomy community, which undertook precise measurements to test Einstein's astronomical predictions. The well-known 1919 British eclipse expeditions that made Einstein famous did not convince most scientists to accept relativity. The 1920s saw numerous attempts to measure light-bending, as well as solar line displacements and even ether-drift. How astronomers approached the ``Einstein problem'' in these early years before and after the First World War, and how the public reacted to what they reported, helped to shape attitudes we hold today about Einstein and his ideas.

Personal Recollections of Albert Einstein

NASA Astrophysics Data System (ADS)

Moszkowski, Steven

2005-03-01

My grandparents were good friends of Albert Einstein in Berlin. Later my parents also were on friendly terms with him. I had the opportunity to meet Einstein four times after my parents and I came to the United States in 1940. My parents and I, on occasion, had correspondence with Einstein and took a few photos of him. Albert Einstein had considerable influence on my development and style of doing physics, as I will discuss.

BOOK REVIEW: Numerical Relativity: Solving Einstein's Equations on the Computer Numerical Relativity: Solving Einstein's Equations on the Computer

NASA Astrophysics Data System (ADS)

Gourgoulhon, Eric

2011-04-01

Numerical relativity is one of the major fields of contemporary general relativity and is developing continually. Yet three years ago, no textbook was available on this subject. The first textbook devoted to numerical relativity, by Alcubierre, appeared in 2008 [1] (cf the CQG review [2]). Now comes the second book, by Baumgarte and Shapiro, two well known players in the field. Inevitably, the two books have some common aspects (otherwise they would not deal with the same topic!). For instance the titles of the first four chapters of Baumgarte and Shapiro are very similar to those of Alcubierre. This arises from some logic inherent to the subject: chapter 1 recaps basic GR, chapter 2 introduces the 3+1 formalism, chapter 3 focuses on the initial data and chapter 4 on the choice of coordinates for the evolution. But there are also many differences between the two books, which actually make them complementary. At first glance the differences are the size (720 pages for Baumgarte and Shapiro vs 464 pages for Alcubierre) and the colour figures in Baumgarte and Shapiro. Regarding the content, Baumgarte and Shapiro address many topics which are not present in Alcubierre's book, such as magnetohydrodynamics, radiative transfer, collisionless matter, spectral methods, rotating stars and post-Newtonian approximation. The main difference regards binary systems: virtually absent from Alcubierre's book (except for binary black hole initial data), they occupy not less than five chapters in Baumgarte and Shapiro's book. In contrast, gravitational wave extraction, various hyperbolic formulations of Einstein's equations and the high-resolution shock-capturing schemes are treated in more depth by Alcubierre. In the first four chapters mentioned above, some distinctive features of Baumgarte and Shapiro's book are the beautiful treatment of Oppenheimer-Snyder collapse in chapter 1, the analogy with Maxwell's equations when discussing the constraints and the evolution equations in

Critical phenomena in the general spherically symmetric Einstein-Yang-Mills system

NASA Astrophysics Data System (ADS)

Maliborski, Maciej; Rinne, Oliver

2018-02-01

We study critical behavior in gravitational collapse of a general spherically symmetric Yang-Mills field coupled to the Einstein equations. Unlike the magnetic ansatz used in previous numerical work, the general Yang-Mills connection has two degrees of freedom in spherical symmetry. This fact changes the phenomenology of critical collapse dramatically. The magnetic sector features both type I and type II critical collapse, with universal critical solutions. In contrast, in the general system type I disappears and the critical behavior at the threshold between dispersal and black hole formation is always type II. We obtain values of the mass scaling and echoing exponents close to those observed in the magnetic sector, however we find some indications that the critical solution differs from the purely magnetic discretely self-similar attractor and exact self-similarity and universality might be lost. The additional "type III" critical phenomenon in the magnetic sector, where black holes form on both sides of the threshold but the Yang-Mills potential is in different vacuum states and there is a mass gap, also disappears in the general system. We support our dynamical numerical simulations with calculations in linear perturbation theory; for instance, we compute quasi-normal modes of the unstable attractor (the Bartnik-McKinnon soliton) in type I collapse in the magnetic sector.

Thickenings and conformal gravity

NASA Astrophysics Data System (ADS)

Lebrun, Claude

1991-07-01

A twistor correspondence is given for complex conformal space-times with vanishing Bach and Eastwood-Dighton tensors; when the Weyl curvature is algebraically general, these equations are precisely the conformal version of Einstein's vacuum equations with cosmological constant. This gives a fully curved version of the linearized correspondence of Baston and Mason [B-M].

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + φ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism.more » Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.« less

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

DOE PAGES

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; ...

2017-07-03

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + φ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism.more » Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.« less

Growth or decay of cosmological inhomogeneities as a function of their equation of state

NASA Astrophysics Data System (ADS)

Comer, G. L.; Deruelle, Nathalie; Langlois, David; Parry, Joe

1994-03-01

We expand Einstein's equations in the synchronous gauge in terms of a purely space-dependent, ``seed,'' metric. The (nonlinear) solution accurately describes a universe inhomogeneous at scales larger than the Hubble radius. We show that the inhomogeneities grow or decay, as time increases, depending on the equation of state for the matter (supposed to be a perfect fluid). We then consider the case when matter is a scalar field with an arbitrary potential. Finally we discuss the generality of the model and show that it is an attractor for a class of generic solutions of Einstein's equations.

Normal versus anomalous self-diffusion in two-dimensional fluids: memory function approach and generalized asymptotic Einstein relation.

PubMed

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-07

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation

NASA Astrophysics Data System (ADS)

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-01

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Field equations from Killing spinors

NASA Astrophysics Data System (ADS)

Açık, Özgür

2018-02-01

From the Killing spinor equation and the equations satisfied by their bilinears, we deduce some well-known bosonic and fermionic field equations of mathematical physics. Aside from the trivially satisfied Dirac equation, these relativistic wave equations in curved spacetimes, respectively, are Klein-Gordon, Maxwell, Proca, Duffin-Kemmer-Petiau, Kähler, twistor, and Rarita-Schwinger equations. This result shows that, besides being special kinds of Dirac fermions, Killing fermions can be regarded as physically fundamental. For the Maxwell case, the problem of motion is analysed in a reverse manner with respect to the studies of Einstein-Groemer-Infeld-Hoffmann and Jean Marie Souriau. In the analysis of the gravitino field, a generalised 3-ψ rule is found which is termed the vanishing trace constraint.

Was Einstein Really a Pacifist? Einstein's Independent, Forward-Thinking, Flexible, and Self-Defined Pacifism

NASA Astrophysics Data System (ADS)

Holmes, Virginia Iris

2005-03-01

Perhaps motivated by an admiration for Einstein and a desire to identify with him, combined with a majority world-view in opposition to pacifism, skeptics may often question whether Einstein was really a pacifist. They might point to the fact that his dramatic contributions to the field of physics at the beginning of the twentieth century made nuclear weapons possible, as well as his 1939 letter to President Franklin D. Roosevelt urging him to develop such weapons before the Nazis would, as examples of at least an inconsistent stance on pacifism across time on Einstein's part. However, as this paper will show, Einstein's pacifism began early in his life, was a deep-seated conviction that he expressed repeatedly across the years, and was an independent pacifism that flowed from his own responses to events around him and contained some original and impressively forward-thinking elements. Moreover, in calling himself a pacifist, as Einstein did, he defined pacifism in his own terms, not according to the standards of others, and this self-defined pacifism included the flexibility to designate the Nazis as a special case that had to be opposed through the use of military violence, in his view. As early as during his childhood, Einstein already disliked competitive games, because of the necessity of winners and losers, and disliked military discipline. In his late thirties, living in Germany during the First World War with a prestigious academic position in Berlin, yet retaining his identity as a Swiss citizen, Einstein joined a small group of four intellectuals who signed the pacifist ``Appeal to the Europeans'' in response to the militarist ``Manifesto to the Civilized World'' signed by 93 German intellectuals. In private, throughout that War, Einstein repeatedly expressed his disgust and sense of alienation at the ``war-enthusiasm'' sentiment of the majority. In the aftermath of the War, Einstein was involved in a German private commission to investigate German war

Quantum statistical relation for black holes in nonlinear electrodynamics coupled to Einstein-Gauss-Bonnet AdS gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miskovic, Olivera; Olea, Rodrigo

2011-03-15

We consider curvature-squared corrections to Einstein-Hilbert gravity action in the form of a Gauss-Bonnet term in D>4 dimensions. In this theory, we study the thermodynamics of charged static black holes with anti-de Sitter (AdS) asymptotics, and whose electric field is described by nonlinear electrodynamics. These objects have received considerable attention in recent literature on gravity/gauge dualities. It is well-known that, within the framework of anti-de Sitter/conformal field theory (AdS/CFT) correspondence, there exists a nonvanishing Casimir contribution to the internal energy of the system, manifested as the vacuum energy for global AdS spacetime in odd dimensions. Because of this reason, wemore » derive a quantum statistical relation directly from the Euclidean action and not from the integration of the first law of thermodynamics. To this end, we employ a background-independent regularization scheme which consists, in addition to the bulk action, of counterterms that depend on both extrinsic and intrinsic curvatures of the boundary (Kounterterm series). This procedure results in a consistent inclusion of the vacuum energy and chemical potential in the thermodynamic description for Einstein-Gauss-Bonnet AdS gravity regardless of the explicit form of the nonlinear electrodynamics Lagrangian.« less

Gravitational catalysis of merons in Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Canfora, Fabrizio; Oh, Seung Hun; Salgado-Rebolledo, Patricio

2017-10-01

We construct regular configurations of the Einstein-Yang-Mills theory in various dimensions. The gauge field is of meron-type: it is proportional to a pure gauge (with a suitable parameter λ determined by the field equations). The corresponding smooth gauge transformation cannot be deformed continuously to the identity. In the three-dimensional case we consider the inclusion of a Chern-Simons term into the analysis, allowing λ to be different from its usual value of 1 /2 . In four dimensions, the gravitating meron is a smooth Euclidean wormhole interpolating between different vacua of the theory. In five and higher dimensions smooth meron-like configurations can also be constructed by considering warped products of the three-sphere and lower-dimensional Einstein manifolds. In all cases merons (which on flat spaces would be singular) become regular due to the coupling with general relativity. This effect is named "gravitational catalysis of merons".

Modulated amplitude waves in collisionally inhomogeneous Bose Einstein condensates

NASA Astrophysics Data System (ADS)

Porter, Mason A.; Kevrekidis, P. G.; Malomed, Boris A.; Frantzeskakis, D. J.

2007-05-01

We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length a subjected to a spatially periodic modulation, a=a(x)=a(x+L). This “collisionally inhomogeneous” BEC is described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of x. We transform this equation into a GP equation with a constant coefficient and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization of the Ince equation. In the small-amplitude limit, we use averaging to construct analytical solutions for modulated amplitude waves (MAWs), whose stability we subsequently examine using both numerical simulations of the original GP equation and fixed-point computations with the MAWs as numerically exact solutions. We show that “on-site” solutions, whose maxima correspond to maxima of a(x), are more robust and likely to be observed than their “off-site” counterparts.

A note on the Hyper-CR equation, and gauged N = 2 supergravity

NASA Astrophysics Data System (ADS)

Dunajski, Maciej; Gutowski, Jan; Sabra, Wafic

2018-05-01

We construct a new class of solutions to the dispersionless hyper-CR equation, and show how any solution to this equation gives rise to a supersymmetric Einstein-Maxwell cosmological space-time in (3 + 1)-dimensions.

Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries

NASA Astrophysics Data System (ADS)

Holst, Michael; Meier, Caleb; Tsogtgerel, G.

2018-01-01

In this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the Einstein constraint equations on compact manifolds with boundary. By building in a natural way on our recent work in Holst and Tsogtgerel (Class Quantum Gravity 30:205011, 2013), and Holst et al. (Phys Rev Lett 100(16):161101, 2008, Commun Math Phys 288(2):547-613, 2009), and also on the work of Maxwell (J Hyperbolic Differ Eqs 2(2):521-546, 2005a, Commun Math Phys 253(3):561-583, 2005b, Math Res Lett 16(4):627-645, 2009) and Dain (Class Quantum Gravity 21(2):555-573, 2004), under reasonable assumptions on the data we prove existence of both near- and far-from-constant mean curvature (CMC) solutions for a class of Robin boundary conditions commonly used in the literature for modeling black holes, with a third existence result for CMC appearing as a special case. Dain and Maxwell addressed initial data engineering for space-times that evolve to contain black holes, determining solutions to the conformal formulation on an asymptotically Euclidean manifold in the CMC setting, with interior boundary conditions representing excised interior black hole regions. Holst and Tsogtgerel compiled the interior boundary results covered by Dain and Maxwell, and then developed general interior conditions to model the apparent horizon boundary conditions of Dainand Maxwell for compact manifolds with boundary, and subsequently proved existence of solutions to the Lichnerowicz equation on compact manifolds with such boundary conditions. This paper picks up where Holst and Tsogtgerel left off, addressing the general non-CMC case for compact manifolds with boundary. As in our previous articles, our focus here is again on low regularity data and on the interaction between different types of boundary conditions. While our work here serves primarily to extend the solution theory for the compact with boundary case, we also develop several technical tools that have

Expanding wave solutions of the Einstein equations that induce an anomalous acceleration into the Standard Model of Cosmology.

PubMed

Temple, Blake; Smoller, Joel

2009-08-25

We derive a system of three coupled equations that implicitly defines a continuous one-parameter family of expanding wave solutions of the Einstein equations, such that the Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology is embedded as a single point in this family. By approximating solutions near the center to leading order in the Hubble length, the family reduces to an explicit one-parameter family of expanding spacetimes, given in closed form, that represents a perturbation of the Standard Model. By introducing a comoving coordinate system, we calculate the correction to the Hubble constant as well as the exact leading order quadratic correction to the redshift vs. luminosity relation for an observer at the center. The correction to redshift vs. luminosity entails an adjustable free parameter that introduces an anomalous acceleration. We conclude (by continuity) that corrections to the redshift vs. luminosity relation observed after the radiation phase of the Big Bang can be accounted for, at the leading order quadratic level, by adjustment of this free parameter. The next order correction is then a prediction. Since nonlinearities alone could actuate dissipation and decay in the conservation laws associated with the highly nonlinear radiation phase and since noninteracting expanding waves represent possible time-asymptotic wave patterns that could result, we propose to further investigate the possibility that these corrections to the Standard Model might be the source of the anomalous acceleration of the galaxies, an explanation not requiring the cosmological constant or dark energy.

Bose-Einstein condensation of the classical axion field in cosmology?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davidson, Sacha; Elmer, Martin, E-mail: s.davidson@ipnl.in2p3.fr, E-mail: m.elmer@ipnl.in2p3.fr

The axion is a motivated cold dark matter candidate, which it would be interesting to distinguish from weakly interacting massive particles. Sikivie has suggested that axions could behave differently during non-linear galaxy evolution, if they form a Bose-Einstein condensate, and argues that ''gravitational thermalisation'' drives them to a Bose-Einstein condensate during the radiation dominated era. Using classical equations of motion during linear structure formation, we explore whether the gravitational interactions of axions can generate enough entropy. At linear order in G{sub N}, we interpret that the principle activities of gravity are to expand the Universe and grow density fluctuations. Tomore » quantify the rate of entropy creation we use the anisotropic stress to estimate a short dissipation scale for axions which does not confirm previous estimates of their gravitational thermalisation rate.« less

Stability of the Einstein static universe in open cosmological models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Canonico, Rosangela; Parisi, Luca; INFN, Sezione di Napoli, GC di Salerno, Via Ponte Don Melillo, I-84081 Baronissi

2010-09-15

The stability properties of the Einstein static solution of general relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein static solutions in the semiclassical regime of loop quantum cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of Horava-Lifshitz gravitymore » under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according to the admitted values of the parameters.« less

Characterization of nonequilibrium states of trapped Bose–Einstein condensates

NASA Astrophysics Data System (ADS)

Yukalov, V. I.; Novikov, A. N.; Bagnato, V. S.

2018-06-01

The generation of different nonequilibrium states in trapped Bose–Einstein condensates is studied by numerically solving the nonlinear Schrödinger equation. Inducing nonequilibrium states by shaking a trap creates the following states: weak nonequilibrium, the state of vortex germs, the state of vortex rings, the state of straight vortex lines, the state of deformed vortices, vortex turbulence, grain turbulence, and wave turbulence. A characterization of nonequilibrium states is advanced by introducing effective temperature, Fresnel number, and Mach number.

Cosmological applications of singular hypersurfaces in general relativity

NASA Astrophysics Data System (ADS)

Laguna-Castillo, Pablo

Three applications to cosmology of surface layers, based on Israel's formalism of singular hypersurfaces and thin shells in general relativity, are presented. Einstein's field equations are analyzed in the presence of a bubble nucleated in vacuum phase transitions within the context of the old inflationary universe scenario. The evolution of a bubble with vanishing surface energy density is studied. It is found that such bubbles lead to a worm-hole matching. Next, the observable four-dimensional universe is considered as a singular hypersurface of discontinuity embedded in a five-dimensional Kaluza-Klein cosmology. It is possible to rewrite the projected five-dimensional Einstein equations on the surface layer in a similar way to the four-dimensional Robertson-Walker cosmology equations. Next, a model is described for an infinite-length, straight U(1) cosmic string as a cylindrical, singular shell enclosing a region of false vacuum. A set of equations is introduced which are required to develop a three-dimensional computer code whose purpose is to study the process of intercommuting cosmic strings with the inclusion of gravitational effects. The outcome is evolution and constraint equations for the gravitational, scalar and gauge field of two initially separated, perpendicular, cosmic strings.

On the validity of Stokes-Einstein and Stokes-Einstein-Debye relations in ionic liquids and ionic-liquid mixtures.

PubMed

Köddermann, Thorsten; Ludwig, Ralf; Paschek, Dietmar

2008-09-15

Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations in the neat ionic liquid (IL) [C(2)mim][NTf(2)] and IL/chloroform mixtures are studied by means of molecular dynamics (MD) simulations. For this purpose, we simulate the translational diffusion coefficients of the cations and anions, the rotational correlation times of the C(2)--H bond in the cation C(2)mim(+), and the viscosities of the whole system. We find that the SE and SED relations are not valid for the pure ionic liquid, nor for IL/chloroform mixtures down to the miscibility gap (at 50 wt % IL). The deviations from both relations could be related to dynamical heterogeneities described by the non-Gaussian parameter alpha(t). If alpha(t) is close to zero, at a concentration of 1 wt % IL in chloroform, both relations become valid. Then, the effective radii and volumes calculated from the SE and SED equations can be related to the structures found in the MD simulations, such as aggregates of ion pairs. Overall, similarities are observed between the dynamical properties of supercooled water and those of ionic liquids.

Einstein for Everyone

ScienceCinema

Piccioni, Robert

2018-04-25

Young Einstein was a rebel who seemed doomed to fail. How did he overcome rejection to become the most famous scientist in history? We will discuss and explain all his theories in plain English and without math, and we will discover how Einstein's achievements impact our lives through DVDs, GPS, iPods, computers and green energy.

Einstein for Everyone

DOE Office of Scientific and Technical Information (OSTI.GOV)

Piccioni, Robert

2010-10-05

Young Einstein was a rebel who seemed doomed to fail. How did he overcome rejection to become the most famous scientist in history? We will discuss and explain all his theories in plain English and without math, and we will discover how Einstein's achievements impact our lives through DVDs, GPS, iPods, computers and green energy.

Einstein's physical strategy, energy conservation, symmetries, and stability: "But Grossmann & I believed that the conservation laws were not satisfied"

NASA Astrophysics Data System (ADS)

Pitts, J. Brian

2016-05-01

Recent work on the history of General Relativity by Renn et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work relate to emerging knowledge (1911-1914) of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance xμ‧ = Mνμ xν to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory (which avoids negative-energies but gets an asymmetric canonical tensor as a result) as on a scalar theory (the Newtonian limit). Einstein's theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom (later called "ghosts" in particle physics). Thus the Entwurf theory fails a 1920s-1930s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work; one might anticipate possible gravitational instability. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting

A noncompact Weyl-Einstein-Yang-Mills model: A semiclassical quantum gravity

NASA Astrophysics Data System (ADS)

Dengiz, Suat

2017-08-01

We construct and study perturbative unitarity (i.e., ghost and tachyon analysis) of a 3 + 1-dimensional noncompact Weyl-Einstein-Yang-Mills model. The model describes a local noncompact Weyl's scale plus SU(N) phase invariant Higgs-like field,conformally coupled to a generic Weyl-invariant dynamical background. Here, the Higgs-like sector generates the Weyl's conformal invariance of system. The action does not admit any dimensionful parameter and genuine presence of de Sitter vacuum spontaneously breaks the noncompact gauge symmetry in an analogous manner to the Standard Model Higgs mechanism. As to flat spacetime, the dimensionful parameter is generated within the dimensional transmutation in quantum field theories, and thus the symmetry is radiatively broken through the one-loop Effective Coleman-Weinberg potential. We show that the mere expectation of reducing to Einstein's gravity in the broken phases forbids anti-de Sitter space to be its stable vacua. The model is unitary in de Sitter and flat vacua around which a massless graviton, N2 - 1 massless scalar bosons, N massless Dirac fermions, N2 - 1 Proca-type massive Abelian and non-Abelian vector bosons are generically propagated.

The Weak-Coupling of Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Zhou, Xiao-Ji; Ma, Zao-Yuan; Chen, Xu-Zong; Wang, Yi-Qiu

2003-04-01

The coherent characteristics of four trapped Bose-Einstein condensates (BEC) conjunct one by one in a ring shape which is divided by two far off-resonant lasers, are studied. Four coupled Gross-Pitaevskii equations are used to describe the dynamics of the system. Two kinds of self-trapping effects are discussed in the coupled BECs, and the phase diagrams for different initial conditions and different coupling strengths are discussed. This study can be used to determine interaction parameters between atoms in BEC. The project supported by National Natural Science Foundation of China under Grant No. 60271003

Einstein's philosophy of physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seeger, R.J.

1979-09-01

Sources of Einstein's philosophical ideas are discussed. Einstein was indebted to Mach and Poincare, and espoused more or less a logical empiricism. He looked upon Nature as real, rational, and understandable, at least to an extent. (RWR)

Inevitable inflation in Einstein-Cartan theory with improved energy-momentum tensor with spin

NASA Technical Reports Server (NTRS)

Fennelly, A. J.; Bradas, James C.; Smalley, Larry L.

1988-01-01

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic, (Bianchi Type-1) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley improved energy momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density. Shear is not effective in preventing inflation in the ECRS model. The relation between fluid vorticity, torsion, reference axis rotation, and shear ellipsoid precession shows through clearly.

Book Review:

NASA Astrophysics Data System (ADS)

Ernst, Frederick J.

2007-06-01

Shortly after Einstein published his general theory of relativity, the spherically symmetric solution of the vacuum field equations was discovered by Karl Schwarzschild, while Hermann Weyl showed that from any axisymmetric solution ψ of the Laplace equation ∇²ψ = 0 (satisfying appropriate boundary conditions) the metric tensor of a static axisymmetric vacuum spacetime can be constructed. In particular, the Schwarzschild solution corresponds to a rather trivial solution of Laplace's equation expressed in terms of prolate spheroidal coordinates. It took about 45 years before Roy Kerr discovered what he called the 'rotating Schwarzschild solution', and an additional five years before I established that from any complex axisymmetric solution \\E of the nonlinear equation (\\Re E)\

Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eberle, Tobias; Centre for Quantum Engineering and Space-Time Research - QUEST, Leibniz Universitaet Hannover, Welfengarten 1, D-30167 Hannover; Haendchen, Vitus

Einstein-Podolsky-Rosen (EPR) entanglement is a criterion that is more demanding than just certifying entanglement. We theoretically and experimentally analyze the low-resource generation of bipartite continuous-variable entanglement, as realized by mixing a squeezed mode with a vacuum mode at a balanced beam splitter, i.e., the generation of so-called vacuum-class entanglement. We find that in order to observe EPR entanglement the total optical loss must be smaller than 33.3 %. However, arbitrarily strong EPR entanglement is generally possible with this scheme. We realize continuous-wave squeezed light at 1550 nm with up to 9.9 dB of nonclassical noise reduction, which is the highestmore » value at a telecom wavelength so far. Using two phase-controlled balanced homodyne detectors we observe an EPR covariance product of 0.502{+-}0.006<1, where 1 is the critical value. We discuss the feasibility of strong Gaussian entanglement and its application for quantum key distribution in a short-distance fiber network.« less

Hamiltonian approach to GR - Part 1: covariant theory of classical gravity

NASA Astrophysics Data System (ADS)

Cremaschini, Claudio; Tessarotto, Massimo

2017-05-01

A challenging issue in General Relativity concerns the determination of the manifestly covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor \\widehat{g}(r)≡ { \\widehat{g}_{μ ν }(r)} solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields x≡ { g,π } obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations. It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably reduced canonical state. As a result, the corresponding Hamilton-Jacobi theory is established in manifestly covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations.

Changes in concepts of time from Aristotle to Einstein

NASA Astrophysics Data System (ADS)

Sachs, Mendel

1996-03-01

The meaning of time and motion is discussed, at first tracing conceptual changes from Aristotle to Galileo/Newton to Einstein. Different views of ‘time’ in 20th century physics are then examined, with primary focus on the revolutionary changes that came with the theory of general relativity. Implications of its new view in all domains of physics are discussed — from elementary particles to cosmology. The special role of Hamilton's quaternion calculus in equations of motion in general relativity is shown.

Implications of Einstein-Weyl Causality on Quantum Mechanics

NASA Astrophysics Data System (ADS)

Bendaniel, David

A fundamental physical principle that has consequences for the topology of space-time is the principle of Einstein-Weyl causality. This also has quantum mechanical manifestations. Borchers and Sen have rigorously investigated the mathematical implications of Einstein-Weyl causality and shown the denumerable space-time Q2 would be implied. They were left with important philosophical paradoxes regarding the nature of the physical real line E, e.g., whether E = R, the real line of mathematics. In order to remove these paradoxes an investigation into a constructible foundation is suggested. We have pursued such a program and find it indeed provides a dense, denumerable space-time and, moreover, an interesting connection with quantum mechanics. We first show that this constructible theory contains polynomial functions which are locally homeomorphic with a dense, denumerable metric space R* and are inherently quantized. Eigenfunctions governing fields can then be effectively obtained by computational iteration. Postulating a Lagrangian for fields in a compactified space-time, we get a general description of which the Schrodinger equation is a special case. From these results we can then also show that this denumerable space-time is relational (in the sense that space is not infinitesimally small if and only if it contains a quantized field) and, since Q2 is imbedded in R*2, it directly fulfills the strict topological requirements for Einstein-Weyl causality. Therefore, the theory predicts that E = R*.

Vacuum fluctuations of the supersymmetric field in curved background

NASA Astrophysics Data System (ADS)

Bilić, Neven; Domazet, Silvije; Guberina, Branko

2012-01-01

We study a supersymmetric model in curved background spacetime. We calculate the effective action and the vacuum expectation value of the energy momentum tensor using a covariant regularization procedure. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density and pressure. Assuming the presence of a cosmic fluid in addition to the vacuum fluctuations of the supersymmetric field an effective equation of state is derived in a self-consistent approach at one loop order. The net effect of the vacuum fluctuations of the supersymmetric fields in the leading adiabatic order is a renormalization of the Newton and cosmological constants.

Nonholonomic relativistic diffusion and exact solutions for stochastic Einstein spaces

NASA Astrophysics Data System (ADS)

Vacaru, S. I.

2012-03-01

We develop an approach to the theory of nonholonomic relativistic stochastic processes in curved spaces. The Itô and Stratonovich calculus are formulated for spaces with conventional horizontal (holonomic) and vertical (nonholonomic) splitting defined by nonlinear connection structures. Geometric models of the relativistic diffusion theory are elaborated for nonholonomic (pseudo) Riemannian manifolds and phase velocity spaces. Applying the anholonomic deformation method, the field equations in Einstein's gravity and various modifications are formally integrated in general forms, with generic off-diagonal metrics depending on some classes of generating and integration functions. Choosing random generating functions we can construct various classes of stochastic Einstein manifolds. We show how stochastic gravitational interactions with mixed holonomic/nonholonomic and random variables can be modelled in explicit form and study their main geometric and stochastic properties. Finally, the conditions when non-random classical gravitational processes transform into stochastic ones and inversely are analyzed.

Spectral Cauchy Characteristic Extraction: Gravitational Waves and Gauge Free News

NASA Astrophysics Data System (ADS)

Handmer, Casey; Szilagyi, Bela; Winicour, Jeff

2015-04-01

We present a fast, accurate spectral algorithm for the characteristic evolution of the full non-linear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate how spectral Cauchy characteristic extraction produces gravitational News without confounding gauge effects. We explain several numerical innovations and demonstrate speed, stability, accuracy, exponential convergence, and consistency with existing methods. We highlight its capability to deliver physical insights in the study of black hole binaries.

Albert Einstein 1879-1955.

ERIC Educational Resources Information Center

Physics Today, 1979

1979-01-01

Celebrates the centennial of Einstein's birth with an eight-page pictorial biography and two special articles: (1) Einstein the catalyst; and (2) Unitary field theories. His special and general theories of relativity and his contributions to quantum physics and other topics are also presented. (HM)

Numerical simulation code for self-gravitating Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Madarassy, Enikő J. M.; Toth, Viktor T.

2013-04-01

We completed the development of simulation code that is designed to study the behavior of a conjectured dark matter galactic halo that is in the form of a Bose-Einstein Condensate (BEC). The BEC is described by the Gross-Pitaevskii equation, which can be solved numerically using the Crank-Nicholson method. The gravitational potential, in turn, is described by Poisson’s equation, that can be solved using the relaxation method. Our code combines these two methods to study the time evolution of a self-gravitating BEC. The inefficiency of the relaxation method is balanced by the fact that in subsequent time iterations, previously computed values of the gravitational field serve as very good initial estimates. The code is robust (as evidenced by its stability on coarse grids) and efficient enough to simulate the evolution of a system over the course of 109 years using a finer (100×100×100) spatial grid, in less than a day of processor time on a contemporary desktop computer. Catalogue identifier: AEOR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOR_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5248 No. of bytes in distributed program, including test data, etc.: 715402 Distribution format: tar.gz Programming language: C++ or FORTRAN. Computer: PCs or workstations. Operating system: Linux or Windows. Classification: 1.5. Nature of problem: Simulation of a self-gravitating Bose-Einstein condensate by simultaneous solution of the Gross-Pitaevskii and Poisson equations in three dimensions. Solution method: The Gross-Pitaevskii equation is solved numerically using the Crank-Nicholson method; Poisson’s equation is solved using the relaxation method. The time evolution of the system is governed by the Gross-Pitaevskii equation; the solution of Poisson�

Einstein: A Historical Perspective

NASA Astrophysics Data System (ADS)

Kormos-Buchwald, Diana

2015-04-01

In late 1915, Albert Einstein (1879-1955) completed as series of papers on a generalized theory of gravitation that were to constitute a major conceptual change in the history of modern physics and the crowning achievement of his scientific career. But this accomplishment came after a decade of intense intellectual struggle and was received with muted enthusiasm. Einstein's previously unpublished writings and massive correspondence, edited by the Einstein Papers Project, provide vivid insights into the historical, personal, and scientific context of the formulation, completion, and reception of GR during the first decades of the 20th century.

Well-posedness of the plasma-vacuum interface problem

NASA Astrophysics Data System (ADS)

Secchi, Paolo; Trakhinin, Yuri

2014-01-01

We consider the free-boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the pre-Maxwell dynamics for the magnetic field. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. The plasma-vacuum system is not isolated from the outside world, because of a given surface current on the fixed boundary that forces oscillations. Under a suitable stability condition satisfied at each point of the initial interface, stating that the magnetic fields on either side of the interface are not collinear, we show the existence and uniqueness of the solution to the nonlinear plasma-vacuum interface problem in suitable anisotropic Sobolev spaces. The proof is based on the results proved in the companion paper (Secchi and Trakhinin 2013 Interfaces Free Boundaries 15 323-57), about the well-posedness of the homogeneous linearized problem and the proof of a basic a priori energy estimate. The proof of the resolution of the nonlinear problem given in the present paper follows from the analysis of the elliptic system for the vacuum magnetic field, a suitable tame estimate in Sobolev spaces for the full linearized equations, and a Nash-Moser iteration.

Beyond Einstein

NASA Astrophysics Data System (ADS)

Hertz, P.

2003-03-01

The Structure and Evolution of the Universe (SEU) theme within NASA's Office of Space Science seeks to explore and understand the dynamic transformations of energy in the Universe - the entire web of biological and physical interactions that determine the evolution of our cosmic habitat. This search for understanding will enrich the human spirit and inspire a new generation of explorers, scientists, and engineers. To that end, NASA's strategic planning process has generated a new Roadmap to enable those goals. Called "Beyond Einstein", this Roadmap identifies three science objectives for the SEU theme: (1) Find out what powered the Big Bang; (2) Observe how black holes manipulate space, time, and matter; and (3) Identify the mysterious dark energy pullingthe Universe apart. These objectives can be realized through a combination of large observatories (Constellation-X, LISA), moderate sized, PI-led missions (the Einstein Probes), and a contuinuing program of technology development, research and analysis, and education/public outreach. In this presentation, NASA's proposed Beyond Einstein Program will be described. The full Roadmap is available at http://universe.nasa.gov/.

Spherically symmetric Einstein-aether perfect fluid models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coley, Alan A.; Latta, Joey; Leon, Genly

We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysicalmore » objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β−) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.« less

New method to generate the solutions of the reduced Einstein equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hou Bo-Yu; Li Wei

In this paper, we present a new transformation in the solution space of the Ernst equation and investigate the relationship between the solutions of the Ernst equation and our transformation. We show that the Ernst equation is invariant under such a transformation; i.e., our transformation can be used to generate the new solutions of the Ernst equation from the old ones. Finally, we discuss the relationship between the Virasoro algebra and this transformation.

Einstein Up in Smoke

NASA Astrophysics Data System (ADS)

Lisle, John

2016-01-01

Albert Einstein's biographers have not explained why he developed the abdominal aortic aneurysm that led to his death. Early conjectures proposed that it was caused by syphilis, without accurate evidence. The present article gives evidence to the contrary, and argues that the principal cause of Einstein's death was smoking.

Einstein as a Missionary of Science

NASA Astrophysics Data System (ADS)

Renn, Jürgen

2013-10-01

The paper reviews Einstein's engagement as a mediator and popularizer of science. It discusses the formative role of popular scientific literature for the young Einstein, showing that not only his broad scientific outlook but also his internationalist political views were shaped by these readings. Then, on the basis of recent detailed studies, Einstein's travels and their impact on the dissemination of relativity theory are examined. These activities as well as Einstein's own popular writings are interpreted in the context of his understanding of science as part of human culture.

Einstein's cosmology review of 1933: a new perspective on the Einstein-de Sitter model of the cosmos

NASA Astrophysics Data System (ADS)

O'Raifeartaigh, Cormac; O'Keeffe, Michael; Nahm, Werner; Mitton, Simon

2015-09-01

We present a first English translation and analysis of a little-known review of relativistic cosmology written by Albert Einstein in late 1932. The article, which was published in 1933 in a book of Einstein papers translated into French, contains a substantial review of static and dynamic relativistic models of the cosmos, culminating in a discussion of the Einstein-de Sitter model. The article offers a valuable contemporaneous insight into Einstein's cosmology in the early 1930s and confirms that his interest lay in the development of the simplest model of the cosmos that could account for observation. The article also confirms that Einstein did not believe that simplified relativistic models could give an accurate description of the early universe.

Universal Themes of Bose-Einstein Condensation

NASA Astrophysics Data System (ADS)

Proukakis, Nick P.; Snoke, David W.; Littlewood, Peter B.

2017-04-01

Foreword; List of contributors; Preface; Part I. Introduction: 1. Universality and Bose-Einstein condensation: perspectives on recent work D. W. Snoke, N. P. Proukakis, T. Giamarchi and P. B. Littlewood; 2. A history of Bose-Einstein condensation of atomic hydrogen T. Greytak and D. Kleppner; 3. Twenty years of atomic quantum gases: 1995-2015 W. Ketterle; 4. Introduction to polariton condensation P. B. Littlewood and A. Edelman; Part II. General Topics: Editorial notes; 5. The question of spontaneous symmetry breaking in condensates D. W. Snoke and A. J. Daley; 6. Effects of interactions on Bose-Einstein condensation R. P. Smith; 7. Formation of Bose-Einstein condensates M. J. Davis, T. M. Wright, T. Gasenzer, S. A. Gardiner and N. P. Proukakis; 8. Quenches, relaxation and pre-thermalization in an isolated quantum system T. Langen and J. Schmiedmayer; 9. Ultracold gases with intrinsic scale invariance C. Chin; 10. Berezinskii-Kosterlitz-Thouless phase of a driven-dissipative condensate N. Y. Kim, W. H. Nitsche and Y. Yamamoto; 11. Superfluidity and phase correlations of driven dissipative condensates J. Keeling, L. M. Sieberer, E. Altman, L. Chen, S. Diehl and J. Toner; 12. BEC to BCS crossover from superconductors to polaritons A. Edelman and P. B. Littlewood; Part III. Condensates in Atomic Physics: Editorial notes; 13. Probing and controlling strongly correlated quantum many-body systems using ultracold quantum gases I. Bloch; 14. Preparing and probing chern bands with cold atoms N. Goldman, N. R. Cooper and J. Dalibard; 15. Bose-Einstein condensates in artificial gauge fields L. J. LeBlanc and I. B. Spielman; 16. Second sound in ultracold atomic gases L. Pitaevskii and S. Stringari; 17. Quantum turbulence in atomic Bose-Einstein condensates N. G. Parker, A. J. Allen, C. F. Barenghi and N. P. Proukakis; 18. Spinor-dipolar aspects of Bose-Einstein condensation M. Ueda; Part IV. Condensates in Condensed Matter Physics: Editorial notes; 19. Bose-Einstein

Nucleation and growth of vortices in a rotating Bose-Einstein condensate.

PubMed

Vorov, O K; Isacker, P Van; Hussein, M S; Bartschat, K

2005-12-02

An analytic solution of the Gross-Pitaevskii equation for a rotating Bose-Einstein condensate of trapped atoms describes the onset of vorticity when the rotational speed is increased, starting with the entry of the first vortex and followed by the formation of growing symmetric Wigner molecules. It explains the staircase of angular momentum jumps and the behavior of the bosonic occupancies observed in numerical studies. The similarity of this behavior and mesoscopic superconductors is discussed.

Gravity as Elasticity of Spacetime:

NASA Astrophysics Data System (ADS)

Padmanabhan, T.

It is very likely that the quantum description of spacetime is quite different from what we perceive at large scales, l≫(Gℏ/c3)1/2. The long wavelength description of spacetime, based on Einstein's equations, is similar to the description of a continuum solid made of a large number of microscopic degrees of freedom. This paradigm provides a novel interpretation of coordinate transformations as deformations of "spacetime solid" and allows one to obtain Einstein's equations as a consistency condition in the long wavelength limit. The entropy contributed by the microscopic degrees of freedom reduces to a pure surface contribution when Einstein's equations are satisfied. The horizons arises as "defects" in the "spacetime solid" (in the sense of well-defined singular points) and contributes an entropy which is one quarter of the horizon area. Finally, the response of the microstructure to vacuum energy leads to a near cancellation of the cosmological constant, leaving behind a tiny fluctuation which matches with the observed value.

The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes

NASA Astrophysics Data System (ADS)

Barnes, A. P.; Lefloch, P. G.; Schmidt, B. G.; Stewart, J. M.

2004-11-01

We propose a new, augmented formulation of the coupled Euler Einstein equations for perfect fluids on plane-symmetric Gowdy spacetimes. The unknowns of the augmented system are the density and velocity of the fluid and the first- and second-order spacetime derivatives of the metric. We solve the Riemann problem for the augmented system, allowing propagating discontinuities in both the fluid variables and the first- and second-order derivatives of the geometry coefficients. Our main result, based on Glimm's random choice scheme, is the existence of solutions with bounded total variation of the Euler Einstein equations, up to the first time where a blow-up singularity (unbounded first-order derivatives of the geometry coefficients) occurs. We demonstrate the relevance of the augmented system for numerical relativity. We also consider general vacuum spacetimes and solve a Riemann problem, by relying on a theorem by Rendall on the characteristic value problem for the Einstein equations.

New 2D dilaton gravity for nonsingular black holes

NASA Astrophysics Data System (ADS)

Kunstatter, Gabor; Maeda, Hideki; Taves, Tim

2016-05-01

We construct a two-dimensional action that is an extension of spherically symmetric Einstein-Lanczos-Lovelock (ELL) gravity. The action contains arbitrary functions of the areal radius and the norm squared of its gradient, but the field equations are second order and obey Birkhoff’s theorem. In complete analogy with spherically symmetric ELL gravity, the field equations admit the generalized Misner-Sharp mass as the first integral that determines the form of the vacuum solution. The arbitrary functions in the action allow for vacuum solutions that describe a larger class of interesting nonsingular black hole spacetimes than previously available.

Einstein and Besso: Not a Partnership of Equals

NASA Astrophysics Data System (ADS)

Janssen, Michel

2005-04-01

In the 1905 special relativity paper Einstein famously acknowledged the help of his friend and colleague Michele Besso. Besso had been an ideal sounding board for Einstein's ideas. During the years that Einstein developed general relativity, Besso was a good deal more than a sounding board. He collaborated with Einstein on calculations of the perihelion motion of Mercury in 1913. His contributions were substantial and would have warranted co-authorship of Einstein's famous paper on Mercury's perihelion of November 1915, in which Besso is not mentioned at all. Besso also alerted Einstein to problems with the early version of general relativity that Einstein had worked out together with Marcel Grossmann. Einstein essentially ignored Besso's warnings. In addition, Besso went out of his way during this period to act as a mediator between a not always appreciative Einstein, living in Berlin with his cousin Elsa who would become his second wife, and his estranged first wife Mileva, living in Zurich with the couple's two young sons. This period is much better documented than the period leading up to the 1905 paper and consequently much more revealing about the nature of the relationship between Einstein and Besso.

Radiative double copy for Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Chester, David

2018-04-01

Recently, a double-copy formalism was used to calculate gravitational radiation from classical Yang-Mills radiation solutions. This work shows that the Yang-Mills theory coupled to a biadjoint scalar field admits a radiative double copy that agrees with solutions in the Einstein-Yang-Mills theory at the lowest finite order. Within this context, the trace-reversed metric h¯μ ν is a natural double copy of the gauge boson Aμ a . This work provides additional evidence that solutions in gauge and gravity theories are related, even though their respective Lagrangians and nonlinear equations of motion appear to be different.

Waveguide quantum electrodynamics in squeezed vacuum

NASA Astrophysics Data System (ADS)

You, Jieyu; Liao, Zeyang; Li, Sheng-Wen; Zubairy, M. Suhail

2018-02-01

We study the dynamics of a general multiemitter system coupled to the squeezed vacuum reservoir and derive a master equation for this system based on the Weisskopf-Wigner approximation. In this theory, we include the effect of positions of the squeezing sources which is usually neglected in the previous studies. We apply this theory to a quasi-one-dimensional waveguide case where the squeezing in one dimension is experimentally achievable. We show that while dipole-dipole interaction induced by ordinary vacuum depends on the emitter separation, the two-photon process due to the squeezed vacuum depends on the positions of the emitters with respect to the squeezing sources. The dephasing rate, decay rate, and the resonance fluorescence of the waveguide-QED in the squeezed vacuum are controllable by changing the positions of emitters. Furthermore, we demonstrate that the stationary maximum entangled NOON state for identical emitters can be reached with arbitrary initial state when the center-of-mass position of the emitters satisfies certain conditions.

Scattering amplitudes in $$\\mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiodaroli, Marco; Gunaydin, Murat; Johansson, Henrik

We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N = 2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N = 2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian andmore » Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at treelevel and one loop. Lastly, the double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes, which are naturally organized as polynomials in the gauge coupling constant.« less

Scattering amplitudes in $$\\mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity

DOE PAGES

Chiodaroli, Marco; Gunaydin, Murat; Johansson, Henrik; ...

2015-01-15

We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N = 2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N = 2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian andmore » Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at treelevel and one loop. Lastly, the double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes, which are naturally organized as polynomials in the gauge coupling constant.« less

Strong Einstein-Podolsky-Rosen steering with unconditional entangled states

NASA Astrophysics Data System (ADS)

Steinlechner, Sebastian; Bauchrowitz, Jöran; Eberle, Tobias; Schnabel, Roman

2013-02-01

In 1935 Schrödinger introduced the terms entanglement and steering in the context of the famous gedanken experiment discussed by Einstein, Podolsky, and Rosen (EPR). Here, we report on a sixfold increase of the observed EPR-steering effect with regard to previous experiments, as quantified by the Reid criterion. We achieved an unprecedented low conditional variance product of about 0.04<1, where 1 is the upper bound below which steering is demonstrated. The steering effect was observed on an unconditional two-mode-squeezed entangled state that contained a total vacuum state contribution of less than 8%, including detection imperfections. Together with the achieved high interference contrast between the entangled state and a bright coherent laser field, our state is compatible with efficient applications in high-power laser interferometers and fiber-based networks for entanglement distribution.

Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term

NASA Astrophysics Data System (ADS)

Deruelle, Nathalie; Merino, Nelson; Olea, Rodrigo

2018-05-01

We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which uses the Chern-Weil theorem plus a dimensional continuation process, such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The boundary term constructed in this paper allows to deal with a general background and is not equivalent to the Gibbons-Hawking-Myers boundary term. However, we show that they coincide if one replaces the background of the Katz procedure by a product manifold. As a first application we show that this Einstein Gauss-Bonnet Katz action yields, without any extra ingredients, the expected mass of the Boulware-Deser black hole.

Integrable pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Ling, Liming; Zhao, Li-Chen

2015-08-01

We study integrable coupled nonlinear Schrödinger equations with pair particle transition between components. Based on exact solutions of the coupled model with attractive or repulsive interaction, we predict that some new dynamics of nonlinear excitations can exist, such as the striking transition dynamics of breathers, new excitation patterns for rogue waves, topological kink excitations, and other new stable excitation structures. In particular, we find that nonlinear wave solutions of this coupled system can be written as a linear superposition of solutions for the simplest scalar nonlinear Schrödinger equation. Possibilities to observe them are discussed in a cigar-shaped Bose-Einstein condensate with two hyperfine states. The results would enrich our knowledge on nonlinear excitations in many coupled nonlinear systems with transition coupling effects, such as multimode nonlinear fibers, coupled waveguides, and a multicomponent Bose-Einstein condensate system.

Can the Stark-Einstein law resolve the measurement problem from an animate perspective?

PubMed

Thaheld, Fred H

2015-09-01

Analysis of the Stark-Einstein law as it applies to the retinal molecule, which is part of the rhodopsin molecule within the rod cells of the retina, reveals that it may provide the solution to the measurement problem from an animate perspective. That it represents a natural boundary where the Schrödinger equation or wave function automatically goes from linear to nonlinear while remaining in a deterministic state. It will be possible in the near future to subject this theory to empirical tests as has been previously proposed. This analysis provides a contrast to the many decades well studied and debated inanimate measurement problem and would represent an addition to the Stark-Einstein law involving information carried by the photon. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

The NASA Beyond Einstein Program

NASA Technical Reports Server (NTRS)

White, Nicholas E.

2006-01-01

Einstein's legacy is incomplete, his theory of General relativity raises -- but cannot answer --three profound questions: What powered the big bang? What happens to space, time, and matter at the edge of a black hole? and What is the mysterious dark energy pulling the Universe apart? The Beyond Einstein program within NASA's Office of Space Science aims to answer these questions, employing a series of missions linked by powerful new technologies and complementary approaches towards shared science goals. The Beyond Einstein program has three linked elements which advance science and technology towards two visions; to detect directly gravitational wave signals from the earliest possible moments of the BIg Bang, and to image the event horizon of a black hole. The central element is a pair of Einstein Great Observatories, Constellation-X and LISA. Constellation-X is a powerful new X-ray observatory dedicated to X-Ray Spectroscopy. LISA is the first spaced based gravitational wave detector. These powerful facilities will blaze new paths to the questions about black holes, the Big Bang and dark energy. The second element is a series of competitively selected Einstein Probes, each focused on one of the science questions and includes a mission dedicated resolving the Dark Energy mystery. The third element is a program of technology development, theoretical studies and education. The Beyond Einstein program is a new element in the proposed NASA budget for 2004. This talk will give an overview of the program and the missions contained within it.

Conversations With Albert Einstein. II

ERIC Educational Resources Information Center

Shankland, R. S.

1973-01-01

Discusses Einstein's views on the role of Michelson-Morley, Fizeau, and Miller experiments in the development of relativity and his attitude toward the theories of new quantum mechanics. Indicates that Einstein's opposition to quantum mechanics is beyond dispute. (CC)

Localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with time–space modulation

NASA Astrophysics Data System (ADS)

Yao, Yu-Qin; Han, Wei; Li, Ji; Liu, Wu-Ming

2018-05-01

Nonlinearity is one of the most remarkable characteristics of Bose–Einstein condensates (BECs). Much work has been done on one- and two-component BECs with time- or space-modulated nonlinearities, while there is little work on spinor BECs with space–time-modulated nonlinearities. In the present paper we investigate localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with nonlinearities dependent on time and space. We solve the three coupled Gross–Pitaevskii equations by similarity transformation and obtain two families of exact matter wave solutions in terms of Jacobi elliptic functions and the Mathieu equation. The localized states of the spinor matter wave describe the dynamics of vector breathing solitons, moving breathing solitons, quasi-breathing solitons and resonant solitons. The results show that one-order vector breathing solitons, quasi-breathing solitons, resonant solitons and the moving breathing solitons ψ ±1 are all stable, but the moving breathing soliton ψ 0 is unstable. We also present the experimental parameters to realize these phenomena in future experiments.

When Art Meets Einstein

ERIC Educational Resources Information Center

Science Scope, 2006

2006-01-01

This article deals with a pale blue sculpture entitled "A New World View", as an homage to the most famous scientist in modern history, Albert Einstein. It has 32 bas-relief squares composed of glass and steel that represent one aspect of the life and legacy of Albert Einstein. Images of children's faces peer out from behind the glass squares,…

Astrophysical observations: lensing and eclipsing Einstein's theories.

PubMed

Bennett, Charles L

2005-02-11

Albert Einstein postulated the equivalence of energy and mass, developed the theory of special relativity, explained the photoelectric effect, and described Brownian motion in five papers, all published in 1905, 100 years ago. With these papers, Einstein provided the framework for understanding modern astrophysical phenomena. Conversely, astrophysical observations provide one of the most effective means for testing Einstein's theories. Here, I review astrophysical advances precipitated by Einstein's insights, including gravitational redshifts, gravitational lensing, gravitational waves, the Lense-Thirring effect, and modern cosmology. A complete understanding of cosmology, from the earliest moments to the ultimate fate of the universe, will require developments in physics beyond Einstein, to a unified theory of gravity and quantum physics.

Curvature tensors unified field equations on SEXn

NASA Astrophysics Data System (ADS)

Chung, Kyung Tae; Lee, Il Young

1988-09-01

We study the curvature tensors and field equations in the n-dimensional SE manifold SEXn. We obtain several basic properties of the vectors S λ and U λ and then of the SE curvature tensor and its contractions, such as a generalized Ricci identity, a generalized Bianchi identity, and two variations of the Bianchi identity satisfied by the SE Einstein tensor. Finally, a system of field equations is discussed in SEXn and one of its particular solutions is constructed and displayed.

Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Zhu-Fang, E-mail: phycui@nju.edu.cn; State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, CAS, Beijing, 100190; Hou, Feng-Yao

2015-07-15

The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial–vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson–Schwinger equations.

Comments on real tachyon vacuum solution without square roots

NASA Astrophysics Data System (ADS)

Arroyo, E. Aldo

2018-01-01

We analyze the consistency of a recently proposed real tachyon vacuum solution without square roots in open bosonic string field theory. We show that the equation of motion contracted with the solution itself is satisfied. Additionally, by expanding the solution in the basis of the curly ℒ0 and the traditional L 0 eigenstates, we evaluate numerically the vacuum energy and obtain a result in agreement with Sen's conjecture.

Λ(t) CDM and the present accelerating expansion of the universe from 5D scalar vacuum

NASA Astrophysics Data System (ADS)

Madriz Aguilar, José Edgar; Zamarripa, J.; Peraza, A.; Licea, J. A.

2017-12-01

In this letter we investigate some consequences of considering our 4D observable universe as locally and isometrically embedded in a 5D spacetime, where gravity is described by a Brans-Dicke theory in vacuum. Once we impose the embedding conditions we obtain that gravity on the 4D spacetime is governed by the Einstein field equations modified by an extra term that can play the role of a dynamical cosmological constant. Two examples were studied. In the first we derive a cosmological model of a universe filled only with a cosmological constant. In the second we obtain a cosmological solution describing a universe filled with matter, radiation and a dynamical cosmological constant. We constrain the model by using the current observational data combination Planck + WP + BAO + SN. The present acceleration in the expansion of the universe is explained by the geometrically induced dynamical cosmological constant avoiding the introduction of a dark energy component and without addressing the underlying cosmological constant problem. Moreover, all 4D matter sources are geometrically induced in the same manner as it is usually done in the Wesson's induced matter theory.

Three-dimensional skyrmions in spin-2 Bose–Einstein condensates

NASA Astrophysics Data System (ADS)

Tiurev, Konstantin; Ollikainen, Tuomas; Kuopanportti, Pekko; Nakahara, Mikio; Hall, David S.; Möttönen, Mikko

2018-05-01

We introduce topologically stable three-dimensional skyrmions in the cyclic and biaxial nematic phases of a spin-2 Bose–Einstein condensate. These skyrmions exhibit exceptionally high mapping degrees resulting from the versatile symmetries of the corresponding order parameters. We show how these structures can be created in existing experimental setups and study their temporal evolution and lifetime by numerically solving the three-dimensional Gross–Pitaevskii equations for realistic parameter values. Although the biaxial nematic and cyclic phases are observed to be unstable against transition towards the ferromagnetic phase, their lifetimes are long enough for the skyrmions to be imprinted and detected experimentally.

Gaussian impurity moving through a Bose-Einstein superfluid

NASA Astrophysics Data System (ADS)

Pinsker, Florian

2017-09-01

In this paper a finite Gaussian impurity moving through an equilibrium Bose-Einstein condensate at T = 0 is studied. The problem can be described by a Gross-Pitaevskii equation, which is solved perturbatively. The analysis is done for systems of 2 and 3 spatial dimensions. The Bogoliubov equation solutions for the condensate perturbed by a finite impurity are calculated in the co-moving frame. From these solutions the total energy of the perturbed system is determined as a function of the width and the amplitude of the moving Gaussian impurity and its velocity. In addition we derive the drag force the finite sized impurity approximately experiences as it moves through the superfluid, which proves the existence of a superfluid phase for finite extensions of the impurities below the speed of sound. Finally we find that the force increases with velocity until an inflection point from which it decreases again in 2 and 3d.

Modified fluctuation-dissipation and Einstein relation at nonequilibrium steady states

NASA Astrophysics Data System (ADS)

Chaudhuri, Debasish; Chaudhuri, Abhishek

2012-02-01

Starting from the pioneering work of Agarwal [G. S. Agarwal, Zeitschrift für PhysikEPJAFV1434-600110.1007/BF01391621 252, 25 (1972)], we present a unified derivation of a number of modified fluctuation-dissipation relations (MFDR) that relate response to small perturbations around nonequilibrium steady states to steady-state correlations. Using this formalism we show the equivalence of velocity forms of MFDR derived using continuum Langevin and discrete master equation dynamics. The resulting additive correction to the Einstein relation is exemplified using a flashing ratchet model of molecular motors.

The happiest thought of Einstein's life.

NASA Astrophysics Data System (ADS)

Heller, M.

It is a commonly told story that Einstein formulated his famous principle of equivalence when thinking about what happens in a freely falling elevator, and that it was an original idea of his genius distinguished by the rare capability to see deep problems in the most ordinary things. In the reading of Einstein's and Ernst Mach's works the author has discovered that it was not a physicist in an elevator which led to the principle of equivalence but rather somebody falling from a roof; moreover, the idea behind the principle was not invented by Einstein himself but rather read by him from the book by Mach entitled The Science of Mechanics. The influence this book had on young Einstein is very well known.

Evolution of the phase-space density and the Jeans scale for dark matter derived from the Vlasov-Einstein equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Piattella, O.F.; Rodrigues, D.C.; Fabris, J.C.

2013-11-01

We discuss solutions of Vlasov-Einstein equation for collisionless dark matter particles in the context of a flat Friedmann universe. We show that, after decoupling from the primordial plasma, the dark matter phase-space density indicator Q = ρ/(σ{sub 1D}{sup 2}){sup 3/2} remains constant during the expansion of the universe, prior to structure formation. This well known result is valid for non-relativistic particles and is not ''observer dependent'' as in solutions derived from the Vlasov-Poisson system. In the linear regime, the inclusion of velocity dispersion effects permits to define a physical Jeans length for collisionless matter as function of the primordial phase-spacemore » density indicator: λ{sub J} = (5π/G){sup 1/2}Q{sup −1/3}ρ{sub dm}{sup −1/6}. The comoving Jeans wavenumber at matter-radiation equality is smaller by a factor of 2-3 than the comoving wavenumber due to free-streaming, contributing to the cut-off of the density fluctuation power spectrum at the lowest scales. We discuss the physical differences between these two scales. For dark matter particles of mass equal to 200 GeV, the derived Jeans mass is 4.3 × 10{sup −6}M{sub ⊙}.« less

Stationary solutions for the nonlinear Schrödinger equation modeling three-dimensional spherical Bose-Einstein condensates in general potentials.

PubMed

Mallory, Kristina; Van Gorder, Robert A

2015-07-01

Stationary solutions for the cubic nonlinear Schrödinger equation modeling Bose-Einstein condensates (BECs) confined in three spatial dimensions by general forms of a potential are studied through a perturbation method and also numerically. Note that we study both repulsive and attractive BECs under similar frameworks in order to deduce the effects of the potentials in each case. After outlining the general framework, solutions for a collection of specific confining potentials of physical relevance to experiments on BECs are provided in order to demonstrate the approach. We make several observations regarding the influence of the particular potentials on the behavior of the BECs in these cases, comparing and contrasting the qualitative behavior of the attractive and repulsive BECs for potentials of various strengths and forms. Finally, we consider the nonperturbative where the potential or the amplitude of the solutions is large, obtaining various qualitative results. When the kinetic energy term is small (relative to the nonlinearity and the confining potential), we recover the expected Thomas-Fermi approximation for the stationary solutions. Naturally, this also occurs in the large mass limit. Through all of these results, we are able to understand the qualitative behavior of spherical three-dimensional BECs in weak, intermediate, or strong confining potentials.

Scattering of massless scalar waves by magnetically charged black holes in Einstein-Yang-Mills-Higgs theory

NASA Astrophysics Data System (ADS)

Gußmann, Alexander

2017-03-01

The existence of the classical black hole solutions of the Einstein-Yang-Mills-Higgs equations with non-Abelian Yang-Mills-Higgs hair implies that not all classical stationary magnetically charged black holes can be uniquely described by their asymptotic characteristics. In fact, in a certain domain of parameters, there exist different spherically-symmetric, non-rotating and asymptotically-flat classical black hole solutions of the Einstein-Yang-Mills-Higgs equations which have the same ADM mass and the same magnetic charge but significantly different geometries in the near-horizon regions. (These are black hole solutions which are described by a Reissner-Nordström metric on the one hand and the black hole solutions with non-Abelian Yang-Mills-Higgs hair which are described by a metric which is not of Reissner-Nordström form on the other hand). One can experimentally distinguish such black holes with the same asymptotic characteristics but different near-horizon geometries classically by probing the near-horizon regions of the black holes. We argue that one way to probe the near-horizon region of a black hole which allows one to distinguish magnetically charged black holes with the same asymptotic characteristics but different near-horizon geometries is by classical scattering of waves. Using the example of a minimally-coupled massless probe scalar field scattered by magnetically charged black holes which can be obtained as solutions of the Einstein-Yang-Mills-Higgs equations with a Higgs triplet and gauge group SU(2) in the limit of an infinite Higgs self-coupling constant we show how, in this case, the scattering cross sections differ for the magnetically charged black holes with different near-horizon geometries but the same asymptotic characteristics. We find in particular that the characteristic glory peaks in the cross sections are located at different scattering angles.

Mass functional for initial data in 4 +1 -dimensional spacetime

NASA Astrophysics Data System (ADS)

Alaee, Aghil; Kunduri, Hari K.

2014-12-01

We consider a broad class of asymptotically flat, maximal initial data sets satisfying the vacuum constraint equations, admitting two commuting rotational symmetries. We construct a mass functional for "t -ϕi"-symmetric data which evaluates to the Arnowitt-Deser-Misner mass. We then show that R ×U (1 )2 -invariant solutions of the vacuum Einstein equations are critical points of this functional amongst this class of data. We demonstrate the positivity of this functional for a class of rod structures which include the Myers-Perry initial data. The construction is a natural extension of Dain's mass functional to D =5 , although several new features arise.

Series expansion of the modified Einstein Procedure

Treesearch

Seema Chandrakant Shah-Fairbank

2009-01-01

This study examines calculating total sediment discharge based on the Modified Einstein Procedure (MEP). A new procedure based on the Series Expansion of the Modified Einstein Procedure (SEMEP) has been developed. This procedure contains four main modifications to MEP. First, SEMEP solves the Einstein integrals quickly and accurately based on a series expansion. Next,...

Einstein for Schools and the General Public

ERIC Educational Resources Information Center

Johansson, K. E.; Kozma, C; Nilsson, Ch

2006-01-01

In April 2005 the World Year of Physics (Einstein Year in the UK and Ireland) was celebrated with an Einstein week in Stockholm House of Science. Seven experiments illustrated Einstein's remarkable work in 1905 on Brownian motion, the photoelectric effect and special relativity. Thirteen school classes with 260 pupils, 30 teachers and 25 members…

Conceptual Development of Einstein's Mass-Energy Relationship

ERIC Educational Resources Information Center

Wong, Chee Leong; Yap, Kueh Chin

2005-01-01

Einstein's special theory of relativity was published in 1905. It stands as one of the greatest intellectual achievements in the history of human thought. Einstein described the equivalence of mass and energy as "the most important upshot of the special theory of relativity" (Einstein, 1919). In this paper, we will discuss the evolution of the…

Spinor Bose-Einstein Condensates of Positronium

NASA Astrophysics Data System (ADS)

Wang, Yi-Hsieh; Anderson, Brandon; Clark, Charles

2014-05-01

Bose-Einstein condensates (BECs) of positronium (Ps) have been of experimental and theoretical interest due to their potential application as the gain medium of a γ-ray laser. Ps BECs are intrinsically spinor due to the presence of ortho-positronium (o-Ps) and para-positronium (p-Ps), whose annihilation lifetimes differ by three orders of magnitude. In this paper, we study the spinor dynamics and annihilation processes in the p-Ps/o-Ps system using both solutions of the time-dependent Gross-Pitaevskii equations and a semiclassical rate-equation approach. The spinor interactions have an O (4) symmetry which is broken to SO (3) by an internal energy difference between o-Ps and p-Ps. For an initially unpolarized condensate, there is a threshold density of ~1019 cm-3 at which spin mixing between o-Ps and p-Ps occurs. Beyond this threshold, there are unstable spatial modes accompanied by spin mixing. To ensure a high production yield above the critical density, a careful choice of external field must be made to avoid the spin mixing instability. NSF Physics Frontiers Center, ARO Atomtronics MURI, DARPA OLE.

Colliding impulsive gravitational waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nutku, Y.; Halil, M.

1977-11-28

We formulate the problem of colliding plane gravitational waves with two polarizations as the harmonic mappings of Riemannian manifolds and construct an exact solution of the vacuum Einstein field equations describing the interaction of colliding impulsive gravitational waves which in the limit of collinear polarization reduces to the solution of Khan and Penrose.

Einstein and the "Crucial" Experiment

ERIC Educational Resources Information Center

Holton, Gerald

1969-01-01

Examines the widespread view that it was the crucial Michelson-Morley experiment that led Einstein to formulate the special relativity theory. From Einstein's writings, evidence is presented that no such direct genetic connection exists. The author suggests that the historian of science must resist the experimenticist's fallacy of imposing a…

2011 Einstein Fellows Chosen

NASA Astrophysics Data System (ADS)

2011-03-01

ASA has announced the selection of the 2011 Einstein Fellows who will conduct research related to NASA's Physics of the Cosmos program, which aims to expand our knowledge of the origin, evolution, and fate of the Universe. The Einstein Fellowship provides support to the awardees for three years, and the Fellows may pursue their research at a host university or research center of their choosing in the United States. The new Fellows will begin their programs in the fall of 2011. The new Einstein Fellows and their host institutions are listed below: * Akos Bogdan (Smithsonian Astrophysical Observatory, Cambridge, Mass.) * Samuel Gralla (University of Maryland, College Park, Md.) * Philip Hopkins (University of California at Berkeley) * Matthew Kunz (Princeton University, Princeton, N.J.) * Laura Lopez (Massachusetts Institute of Technology, Cambridge, Mass.) * Amy Reines (National Radio Astronomy Observatory, Charlottesville, Virg.) * Rubens Reis (University of Michigan, Ann Arbor) * Ken Shen (Lawrence Berkeley National Laboratory, Berkeley, Calif.) * Jennifer Siegal-Gaskins (California Institute of Technology, Pasadena) * Lorenzo Sironi (Harvard University, Cambridge, Mass.) NASA has two other astrophysics theme-based fellowship programs: the Sagan Fellowship Program, which supports research into exoplanet exploration, and the Hubble Fellowship Program, which supports research into cosmic origins. More information on the Einstein Fellowships can be found at: http://cxc.harvard.edu/fellows/

Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary

NASA Astrophysics Data System (ADS)

Albanese, Guglielmo; Rigoli, Marco

2017-12-01

We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary (M , ∂ M , 〈 , 〉) and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for the Einstein-scalar field equations of General Relativity in the framework of the so called Conformal Method.

Magnetic monopoles, Galilean invariance, and Maxwell's equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crawford, F.S.

1992-02-01

Maxwell's equations have space reserved for magnetic monopoles. Whether or not they exist in our part of the universe, monopoles provide a useful didactic tool to help us recognize relations among Maxwell's equations less easily apparent in the approach followed by many introductory textbooks, wherein Coulomb's law, Biot and Savart's law, Ampere's law, Faraday's law, Maxwell's displacement current, etc., are introduced independently, as demanded by experiment.'' Instead a conceptual path that deduces all of Maxwell's equations from the near-minimal set of assumptions: (a) Inertial frames exist, in which Newton's laws hold, to a first approximation; (b) the laws of electrodynamicsmore » are Galilean invariant---i.e., they have the same form in every inertial frame, to a first approximation; (c) magnetic poles (as well as the usual electric charges) exist; (d) the complete Lorentz force on an electric charge is known; (e) the force on a monopole at rest is known; (f) the Coulomb-like field produced by a resting electric charge and by a resting monopole are known. Everything else is deduced. History is followed in the assumption that Newtonian mechanics have been discovered, but not special relativity. (Only particle velocities {ital v}{much lt}{ital c} are considered.) This ends up with Maxwell's equations (Maxwell did not need special relativity, so why should we,) but facing Einstein's paradox, the solution of which is encapsulated in the Einstein velocity-addition formula.« less

Bose–Einstein condensation temperature of finite systems

NASA Astrophysics Data System (ADS)

Xie, Mi

2018-05-01

In studies of the Bose–Einstein condensation of ideal gases in finite systems, the divergence problem usually arises in the equation of state. In this paper, we present a technique based on the heat kernel expansion and zeta function regularization to solve the divergence problem, and obtain the analytical expression of the Bose–Einstein condensation temperature for general finite systems. The result is represented by the heat kernel coefficients, where the asymptotic energy spectrum of the system is used. Besides the general case, for systems with exact spectra, e.g. ideal gases in an infinite slab or in a three-sphere, the sums of the spectra can be obtained exactly and the calculation of corrections to the critical temperatures is more direct. For a system confined in a bounded potential, the form of the heat kernel is different from the usual heat kernel expansion. We show that as long as the asymptotic form of the global heat kernel can be found, our method works. For Bose gases confined in three- and two-dimensional isotropic harmonic potentials, we obtain the higher-order corrections to the usual results of the critical temperatures. Our method can also be applied to the problem of generalized condensation, and we give the correction of the boundary on the second critical temperature in a highly anisotropic slab.

Albert Einstein's Magic Mountain: An Aarau Education*

NASA Astrophysics Data System (ADS)

Hunziker, Herbert

2015-03-01

For economic reasons, the electrotechnical factory J. Einstein & Cie. (co-owned by Albert Einstein's father Hermann) had to be closed in the summer of 1894. While Albert's parents emigrated to Italy to build a new existence, he remained in Munich to complete his studies at the Gymnasium. Left behind, however, he had a difficult time with what he considered the rigid educational practices at the Munich Luitpold-Gymnasium and quit without a diploma. The present article discusses Einstein's richly winding path to the Aargau Cantonal School (Switzerland), especially its history and educational philosophy during the time of his stay in Aarau. There, Einstein met some outstanding teachers, who could serve him as models of scholars and human beings. In spite of Einstein's distinct independence of mind, these personalities may well have had a significant influence on the alignment of his inner compass.

Exact analysis of surface field reduction due to field-emitted vacuum space charge, in parallel-plane geometry, using simple dimensionless equations

NASA Astrophysics Data System (ADS)

Forbes, Richard G.

2008-10-01

This paper reports (a) a simple dimensionless equation relating to field-emitted vacuum space charge (FEVSC) in parallel-plane geometry, namely 9ζ2θ2-3θ-4ζ+3=0, where ζ is the FEVSC "strength" and θ is the reduction in emitter surface field (θ =field-with/field-without FEVSC), and (b) the formula j =9θ2ζ/4, where j is the ratio of emitted current density JP to that predicted by Child's law. These equations apply to any charged particle, positive or negative, emitted with near-zero kinetic energy. They yield existing and additional basic formulas in planar FEVSC theory. The first equation also yields the well-known cubic equation describing the relationship between JP and applied voltage; a method of analytical solution is described. Illustrative FEVSC effects in a liquid metal ion source and in field electron emission are discussed. For Fowler-Nordheim plots, a "turn-over" effect is predicted in the high FEVSC limit. The higher the voltage-to-local-field conversion factor for the emitter concerned, then the higher is the field at which turn over occurs. Past experiments have not found complete turn over; possible reasons are noted. For real field emitters, planar theory is a worst-case limit; however, adjusting ζ on the basis of Monte Carlo calculations might yield formulae adequate for real situations.

Einstein Session of the Pontifical Academy.

ERIC Educational Resources Information Center

Science, 1980

1980-01-01

The texts of four speeches, given at the 1979 Einstein Session of the Pontifical Academy held in Rome, are presented. Each address relates to some aspect of the life and times of Albert Einstein. (SA)

Probing quantum gravity through exactly soluble midi-superspaces I

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ashtekar, A.; Pierri, M.

1996-12-01

It is well-known that the Einstein-Rosen solutions to the 3+1- dimensional vacuum Einstein{close_quote}s equations are in one to one correspondence with solutions of 2+1-dimensional general relativity coupled to axi-symmetric, zero rest mass scalar fields. We first re-examine the quantization of this midi-superspace paying special attention to the asymptotically flat boundary conditions and to certain functional analytic subtleties associated with regularization. We then use the resulting quantum theory to analyze several conceptual and technical issues of quantum gravity. {copyright} {ital 1996 American Institute of Physics.}

Relations between nonlinear Riccati equations and other equations in fundamental physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-10-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.

BOOK REVIEW: Once Upon Einstein

NASA Astrophysics Data System (ADS)

Giannetto, E.

2007-07-01

Thibault Damour is a theoretical physicist, and a member of the French Academy of Sciences. This book is the translation, by Eric Novak, of the original French Si Einstein m'etait conté (Le Cherche Midi, 2005). It is neither a book of theoretical physics nor a biography of Einstein. It is not a book of history nor philosophy of science. In Damour's words it was written to encourage the reader to share with Einstein `those times when he understood some part of the hidden order of the universe'. It is a relatively short book, written in a very fluent style, but it deals with all the major problems and achievements of Einstein's works. Starting from special relativity, it continues with general relativity, quantum theories, unified field theory and a brief overview of the actual research related to Einstein's legacy. It is essentially a popular science book with some related exploration in history and philosophy to interpret physical theories. The most important problem discussed by Damour is the nature of time. On this subject, there is a very interesting short paragraph (pp 33--35) dedicated to the reception of the relativity idea by the great writer Marcel Proust and its counterpart within À la Recherche du Temps Perdu. A correct discussion of the implications of a relativistic time should imply the distinction of the different possible interpretations of this concept. Damour seems to conclude that only one interpretation is possible: `time does not exist', flowing of time is an illusion. One has to know that Einstein's ideas on time were related to Spinoza's perspective of a knowledge sub specie aeternitatis. However, other interpretations are possible and are related to the idea of time as an actuality. Damour speaks about the controversy between Einstein and Bergson, but Bergson is considered as a philosopher who did not understand relativity. This philosophical problem of relativistic time is indeed related to a historical problem briefly discussed by Damour

Einstein 1905-1955: His Approach to Physics

NASA Astrophysics Data System (ADS)

Damour, Thibault

We review Einstein's epistemological conceptions, and indicate their philosophical roots. The particular importance of the ideas of Hume, Kant, Mach, and Poincaré is highlighted. The specific characteristics of Einstein's approach to physics are underlined. Lastly, we consider the practical application of Einstein's methodological principles to the two theories of relativity, and to quantum theory. We emphasize a Kantian approach to quantum theory.

Dyonic Flux Tube Structure of Nonperturbative QCD Vacuum

NASA Astrophysics Data System (ADS)

Chandola, H. C.; Pandey, H. C.

We study the flux tube structure of the nonperturbative QCD vacuum in terms of its dyonic excitations by using an infrared effective Lagrangian and show that the dyonic condensation of QCD vacuum has a close connection with the process of color confinement. Using the fiber bundle formulation of QCD, the magnetic symmetry condition is presented in a gauge covariant form and the gauge potential has been constructed in terms of the magnetic vectors on global sections. The dynamical breaking of the magnetic symmetry has been shown to lead the dyonic condensation of QCD vacuum in the infrared energy sector. Deriving the asymptotic solutions of the field equations in the dynamically broken phase, the dyonic flux tube structure of QCD vacuum is explored which has been shown to lead the confinement parameters in terms of the vector and scalar mass modes of the condensed vacuum. Evaluating the charge quantum numbers and energy associated with the dyonic flux tube solutions, the effect of electric excitation of monopole is analyzed using the Regge slope parameter (as an input parameter) and an enhancement in the dyonic pair correlations and the confining properties of QCD vacuum in its dyonically condensed mode has been demonstrated.

Einstein's 1919 View

NASA Astrophysics Data System (ADS)

Goradia, Shantilal

2012-10-01

When Rutherford discovered the nuclear force in 1919, he felt the force he discovered reflected some deviation of Newtonian gravity. Einstein too in his 1919 paper published the failure of the general relativity and Newtonian gravity to explain nuclear force and, in his concluding remarks, he retracted his earlier introduction of the cosmological constant. Consistent with his genius, we modify Newtonian gravity as probabilistic gravity using natural Planck units for a realistic study of nature. The result is capable of expressing both (1) nuclear force [strong coupling], and (2) Newtonian gravity in one equation, implying in general, in layman's words, that gravity is the cumulative effect of all quantum mechanical forces which are impossible to measure at long distances. Non discovery of graviton and quantum gravity silently support our findings. Continuing to climb on the shoulders of the giants enables us to see horizons otherwise unseen, as reflected in our book: ``Quantum Consciousness - The Road to Reality,'' and physics/0210040, where we derive the fine structure constant as a function of the age of the universe in Planck times consistent with Gamow's hint, using natural logarithm consistent with Feynman's hint.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Opanchuk, B.; Drummond, P. D.

2013-04-01

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such as quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.

Unification of the general non-linear sigma model and the Virasoro master equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boer, J. de; Halpern, M.B.

1997-06-01

The Virasoro master equation describes a large set of conformal field theories known as the affine-Virasoro constructions, in the operator algebra (affinie Lie algebra) of the WZW model, while the einstein equations of the general non-linear sigma model describe another large set of conformal field theories. This talk summarizes recent work which unifies these two sets of conformal field theories, together with a presumable large class of new conformal field theories. The basic idea is to consider spin-two operators of the form L{sub ij}{partial_derivative}x{sup i}{partial_derivative}x{sup j} in the background of a general sigma model. The requirement that these operators satisfymore » the Virasoro algebra leads to a set of equations called the unified Einstein-Virasoro master equation, in which the spin-two spacetime field L{sub ij} cuples to the usual spacetime fields of the sigma model. The one-loop form of this unified system is presented, and some of its algebraic and geometric properties are discussed.« less

Books on Einstein--Collectors' Delight

ERIC Educational Resources Information Center

Khoon, Koh Aik; Jalal, Azman; Abd-Shukor, R.; Yatim, Baharudin; Talib, Ibrahim Abu; Daud, Abdul Razak; Samat, Supian

2009-01-01

A survey of thirteen books on Einstein is presented. Its gives an idea on how much is written about the man and how frequent are the publications. The year 2005 saw the most publications. It is the centenary for the Miraculous Year. Interestingly some books can just sustain their readers' interest with just words. Einstein comes alive with the…

Cohomogeneity-one solutions in Einstein-Maxwell-dilaton gravity

NASA Astrophysics Data System (ADS)

Lim, Yen-Kheng

2017-05-01

The field equations for Einstein-Maxwell-dilaton gravity in D dimensions are reduced to an effective one-dimensional system under the influence of exponential potentials. Various cases where exact solutions can be found are explored. With this procedure, we present interesting solutions such as a one-parameter generalization of the dilaton-Melvin spacetime and a three-parameter solution that interpolates between the Reissner-Nordström and Bertotti-Robinson solutions. This procedure also allows simple, alternative derivations of known solutions such as the Lifshitz spacetime and the planar anti-de Sitter naked singularity. In the latter case, the metric is cast in a simpler form which reveals the presence of an additional curvature singularity.

Electric and magnetic dipoles in the Lorentz and Einstein-Laub formulations of classical electrodynamics

NASA Astrophysics Data System (ADS)

Mansuripur, Masud

2015-01-01

The classical theory of electrodynamics cannot explain the existence and structure of electric and magnetic dipoles, yet it incorporates such dipoles into its fundamental equations, simply by postulating their existence and properties, just as it postulates the existence and properties of electric charges and currents. Maxwell's macroscopic equations are mathematically exact and self-consistent differential equations that relate the electromagnetic (EM) field to its sources, namely, electric charge-density 𝜌𝜌free, electric current-density 𝑱𝑱free, polarization 𝑷𝑷, and magnetization 𝑴𝑴. At the level of Maxwell's macroscopic equations, there is no need for models of electric and magnetic dipoles. For example, whether a magnetic dipole is an Amperian current-loop or a Gilbertian pair of north and south magnetic monopoles has no effect on the solution of Maxwell's equations. Electromagnetic fields carry energy as well as linear and angular momenta, which they can exchange with material media—the seat of the sources of the EM field—thereby exerting force and torque on these media. In the Lorentz formulation of classical electrodynamics, the electric and magnetic fields, 𝑬𝑬 and 𝑩𝑩, exert forces and torques on electric charge and current distributions. An electric dipole is then modeled as a pair of electric charges on a stick (or spring), and a magnetic dipole is modeled as an Amperian current loop, so that the Lorentz force law can be applied to the corresponding (bound) charges and (bound) currents of these dipoles. In contrast, the Einstein-Laub formulation circumvents the need for specific models of the dipoles by simply providing a recipe for calculating the force- and torque-densities exerted by the 𝑬𝑬 and 𝑯𝑯 fields on charge, current, polarization and magnetization. The two formulations, while similar in many respects, have significant

On the stability of dyons and dyonic black holes in Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Nolan, Brien C.; Winstanley, Elizabeth

2016-02-01

We investigate the stability of four-dimensional dyonic soliton and black hole solutions of {su}(2) Einstein-Yang-Mills theory in anti-de Sitter space. We prove that, in a neighbourhood of the embedded trivial (Schwarzschild-)anti-de Sitter solution, there exist non-trivial dyonic soliton and black hole solutions of the field equations which are stable under linear, spherically symmetric, perturbations of the metric and non-Abelian gauge field.

Equivalent off-diagonal cosmological models and ekpyrotic scenarios in -modified, massive, and einstein gravity

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2015-04-01

We reinvestigate how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive and -modified gravity using the anholonomic frame deformation method. New classes of locally anisotropic and (in-) homogeneous cosmological metrics are constructed with open and closed spatial geometries. By resorting to such solutions, we show that they describe the late time acceleration due to effective cosmological terms induced by nonlinear off-diagonal interactions, possible modifications of the gravitational action and graviton mass. The cosmological metrics and related Stückelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaître-Robertson-Walker (FLRW) coordinates. The solutions include matter, graviton mass, and other effective sources modeling nonlinear gravitational and matter field interactions with polarization of physical constants and deformations of metrics, which may explain dark energy and dark matter effects. However, we argue that it is not always necessary to modify gravity if we consider the effective generalized Einstein equations with nontrivial vacuum and/or non-minimal coupling with matter. Indeed, we state certain conditions when such configurations mimic interesting solutions in general relativity and modifications, for instance, when we can extract the general Painlevé-Gullstrand and FLRW metrics. In a more general context, we elaborate on a reconstruction procedure for off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes. Finally, open issues and further perspectives are discussed.

Perturbation of a planetary orbit by the Lambda-term (dark energy) in Einstein equations

NASA Astrophysics Data System (ADS)

Dumin, Yurii

The problem of cosmological influences at small (e.g. interplanetary) scales is discussed for a few decades, starting from the early 1930's, but still remains unsolved definitively by now [1]. This subject became especially topical in the context of the dark-energy-dominated cosmology, because the commonly-used arguments against the local Hubble expansion (such as Einstein-Straus theorem [2]) are inapplicable when the most contribution to the energy density of the Universe comes from the perfectly-uniform dark energy (Lambda-term). Moreover, there are some empirical evidences in favor of the local cosmological influences. For example, inclusion of the local Hubble expansion into dynamics of the Earth-Moon system enables us to resolve a long-standing discrepancy in the rates of secular increase of the lunar semi-major axis (a) mea-sured by the lunar laser ranging and (b) derived from the astrometric observations of the Earth's rotation deceleration [3, 4]. The aim of the present report is to provide a detailed mathematical treatment of the respective two-body problem in the framework of General Relativity, which is based on the Kottler metric reduced to the Robertson-Walker cosmological asymptotics, as outlined in our earlier work [5]. References: 1. W.B. Bonnor. Gen. Rel. Grav., v.32, p.1005 (2000). 2. A. Einstein and E.G. Straus. Rev. Mod. Phys., v.17, p.120 (1945). 3. Yu.V. Dumin. Adv. Space Res., v.31, p.2461 (2003). 4. Yu.V. Dumin. In Proc. 11th Marcel Grossmann Meeting on General Relativity, World Sci., Singapore, p.1752 (2008). 5. Yu.V. Dumin. Phys. Rev. Lett., v.98, p.059001 (2007).

Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Ivanov, S. K.; Kamchatnov, A. M.; Congy, T.; Pavloff, N.

2017-12-01

We provide a classification of the possible flows of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single polarization mode (also denoted as "magnetic excitation") obeying a system of equations equivalent to the Landau-Lifshitz equation for an easy-plane ferromagnet. We present the full set of one-phase periodic solutions. The corresponding Whitham modulation equations are obtained together with formulas connecting their solutions with the Riemann invariants of the modulation equations. The problem is not genuinely nonlinear, and this results in a non-single-valued mapping of the solutions of the Whitham equations with physical wave patterns as well as the appearance of interesting elements—contact dispersive shock waves—that are absent in more standard, genuinely nonlinear situations. Our analytic results are confirmed by numerical simulations.

Exact anisotropic viscous fluid solutions of Einstein's equations

NASA Astrophysics Data System (ADS)

Goenner, H. F. M.; Kowalewski, F.

1989-05-01

A method for obtaining anisotropic, rotationless viscous fluid matter solutions of Bianchi type I and Segré type [1, 111] with the barotropic equation of state is presented. Solutions for which the anisotropy decreases exponentially or with a power law as well as solutions with average Hubble parameterH ˜t -1 are discussed. Also, a class of solutions with constant anisotropy and Bianchi type VIh is found. The dominant energy condition holds and the transport coefficients show the right sign.

Nakedly singular non-vacuum gravitating equilibrium states

NASA Astrophysics Data System (ADS)

Woszczyna, Andrzej; Kutschera, Marek; Kubis, Sebastian; Czaja, Wojciech; Plaszczyk, Piotr; Golda, Zdzisław A.

2016-01-01

Non-vacuum static spherically symmetric spacetimes with central point-like repulsive gravity sources are investigated. Both the symmetries of spacetime and the degree of irregularity of curvature invariants, are the same as for the Schwarzschild case. The equilibrium configurations are modelled using the neutron star polytrope equation of state.

Singularity-free solutions for anisotropic charged fluids with Chaplygin equation of state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rahaman, Farook; Ray, Saibal; Jafry, Abdul Kayum

2010-11-15

We extend the Krori-Barua analysis of the static, spherically symmetric, Einstein-Maxwell field equations and consider charged fluid sources with anisotropic stresses. The inclusion of a new variable (tangential pressure) allows the use of a nonlinear, Chaplygin-type equation of state with coefficients fixed by the matching conditions at the boundary of the source. Some physical features are briefly discussed.

Application of Ruze Equation for Inflatable Aperture Antennas

NASA Technical Reports Server (NTRS)

Welch, Bryan W.

2008-01-01

Inflatable aperture reflector antennas are an emerging technology that NASA is investigating for potential uses in science and exploration missions. As inflatable aperture antennas have not been proven fully qualified for space missions, they must be characterized properly so that the behavior of the antennas can be known in advance. To properly characterize the inflatable aperture antenna, testing must be performed in a relevant environment, such as a vacuum chamber. Since the capability of having a radiofrequency (RF) test facility inside a vacuum chamber did not exist at NASA Glenn Research Center, a different methodology had to be utilized. The proposal to test an inflatable aperture antenna in a vacuum chamber entailed performing a photogrammetry study of the antenna surface by using laser ranging measurements. A root-mean-square (rms) error term was derived from the photogrammetry study to calculate the antenna surface loss as described by the Ruze equation. However, initial testing showed that problems existed in using the Ruze equation to calculate the loss due to errors on the antenna surface. This study utilized RF measurements obtained in a near-field antenna range and photogrammetry data taken from a laser range scanner to compare the expected performance of the test antenna (via the Ruze equation) with the actual RF patterns and directivity measurements. Results showed that the Ruze equation overstated the degradation in the directivity calculation. Therefore, when the photogrammetry study is performed on the test antennas in the vacuum chamber, a more complex equation must be used in light of the fact that the Ruze theory overstates the loss in directivity for inflatable aperture reflector antennas.

Stability and Metastability of Trapless Bose-Einstein Condensates and Quantum Liquids

NASA Astrophysics Data System (ADS)

Zloshchastiev, Konstantin G.

2017-07-01

Various kinds of Bose-Einstein condensates are considered, which evolve without any geometric constraints or external trap potentials including gravitational. For studies of their collective oscillations and stability, including the metastability and macroscopic tunneling phenomena, both the variational approach and the Vakhitov-Kolokolov (VK) criterion are employed; calculations are done for condensates of an arbitrary spatial dimension. It is determined that that the trapless condensate described by the logarithmic wave equation is essentially stable, regardless of its dimensionality, while the trapless condensates described by wave equations of a polynomial type with respect to the wavefunction, such as the Gross-Pitaevskii (cubic), cubic-quintic, and so on, are at best metastable. This means that trapless "polynomial" condensates are unstable against spontaneous delocalization caused by fluctuations of their width, density and energy, leading to a finite lifetime.

Size quantization in high-temperature superconducting cuprates and a link to Einstein's diffusion law

NASA Astrophysics Data System (ADS)

Roeser, H. P.; Bohr, A.; Haslam, D. T.; López, J. S.; Stepper, M.; Nikoghosyan, A. S.

2012-07-01

Optimum doping of high-temperature superconductors (HTSC) defines a superconducting unit volume for each HTSC. For a single-mode HTSC, e.g., a cuprate with one CuO2 plane, the volume is given by Vsc=cx2, where c is the unit cell height and x the doping distance. The experimental resistivity at Tc is connected to the structure by ρ(exp)≈c×h/(2e2). Combining this result with the classical definition of resistivity leads to an equation similar to Einstein's diffusion law x2/(2τ)=h/(2Meff)=D, where τ is the relaxation time, Meff=2me and D the diffusion constant. It has also been shown that the mean free path d=x. The Einstein-Smoluchowski diffusion relation D=μkBTc provides a connection to Tc.

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

Thermodynamics of a Higher Dimensional Noncommutative Inspired Anti-de Sitter-Einstein-Born-Infeld Black Hole

NASA Astrophysics Data System (ADS)

González, Angélica; Linares, Román; Maceda, Marco; Sánchez-Santos, Oscar

2018-04-01

We analyze noncommutative deformations of a higher dimensional anti-de Sitter-Einstein-Born-Infeld black hole. Two models based on noncommutative inspired distributions of mass and charge are discussed and their thermodynamical properties such as the equation of state are explicitly calculated. In the (3 + 1)-dimensional case the Gibbs energy function of each model is used to discuss the presence of phase transitions.

Freud's superpotential in general relativity and in Einstein-Cartan theory

NASA Astrophysics Data System (ADS)

Böhmer, Christian G.; Hehl, Friedrich W.

2018-02-01

The identification of a suitable gravitational energy in theories of gravity has a long history, and it is well known that a unique answer cannot be given. In the first part of this paper we present a streamlined version of the derivation of Freud's superpotential in general relativity. It is found if we once integrate the gravitational field equation by parts. This allows us to extend these results directly to the Einstein-Cartan theory. Interestingly, Freud's original expression, first stated in 1939, remains valid even when considering gravitational theories in Riemann-Cartan or, more generally, in metric-affine spacetimes.

Einstein's Universe.

ERIC Educational Resources Information Center

Carlson, Eric; Wald, Robert

1979-01-01

Presents a guide to be used by students and teachers in conjunction with a television program about Einstein. Provides general information about special and general relativity, and the universe. Includes questions for discussion after each section and a bibliography. (MA)

Feshbach resonance management for Bose-Einstein condensates.

PubMed

Kevrekidis, P G; Theocharis, G; Frantzeskakis, D J; Malomed, Boris A

2003-06-13

An experimentally realizable scheme of periodic sign-changing modulation of the scattering length is proposed for Bose-Einstein condensates similar to dispersion-management schemes in fiber optics. Because of controlling the scattering length via the Feshbach resonance, the scheme is named Feshbach-resonance management. The modulational-instability analysis of the quasiuniform condensate driven by this scheme leads to an analog of the Kronig-Penney model. The ensuing stable localized structures are found. These include breathers, which oscillate between the Thomas-Fermi and Gaussian configuration, or may be similar to the 2-soliton state of the nonlinear Schrödinger equation, and a nearly static state ("odd soliton") with a nested dark soliton. An overall phase diagram for breathers is constructed, and full stability of the odd solitons is numerically established.

Sonic horizon formation for oscillating Bose-Einstein condensates in isotropic harmonic potential

PubMed Central

Wang, Ying; Zhou, Yu; Zhou, Shuyu

2016-01-01

We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study. PMID:27922129

Evaluating operational vacuum for landfill biogas extraction.

PubMed

Fabbricino, Massimiliano

2007-01-01

This manuscript proposes a practical methodology for estimating the operational vacuum for landfill biogas extraction from municipal landfills. The procedure is based on two sub-models which simulate landfill gas production from organic waste decomposition and distribution of gas pressure and gas movement induced by suction at a blower station. The two models are coupled in a single mass balance equation, obtaining a relationship between the operational vacuum and the amount of landfill gas that can be extracted from an assigned system of vertical wells. To better illustrate the procedure, it is applied to a case study, where a good agreement between simulated and measured data, within +/- 30%, is obtained.

Bose-Einstein condensation in microgravity.

PubMed

van Zoest, T; Gaaloul, N; Singh, Y; Ahlers, H; Herr, W; Seidel, S T; Ertmer, W; Rasel, E; Eckart, M; Kajari, E; Arnold, S; Nandi, G; Schleich, W P; Walser, R; Vogel, A; Sengstock, K; Bongs, K; Lewoczko-Adamczyk, W; Schiemangk, M; Schuldt, T; Peters, A; Könemann, T; Müntinga, H; Lämmerzahl, C; Dittus, H; Steinmetz, T; Hänsch, T W; Reichel, J

2010-06-18

Albert Einstein's insight that it is impossible to distinguish a local experiment in a "freely falling elevator" from one in free space led to the development of the theory of general relativity. The wave nature of matter manifests itself in a striking way in Bose-Einstein condensates, where millions of atoms lose their identity and can be described by a single macroscopic wave function. We combine these two topics and report the preparation and observation of a Bose-Einstein condensate during free fall in a 146-meter-tall evacuated drop tower. During the expansion over 1 second, the atoms form a giant coherent matter wave that is delocalized on a millimeter scale, which represents a promising source for matter-wave interferometry to test the universality of free fall with quantum matter.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Opanchuk, B.; Drummond, P. D.

2013-04-15

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such asmore » quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.« less

Delayed collapses of Bose-Einstein condensates in relation to anti-de Sitter gravity.

PubMed

Biasi, Anxo F; Mas, Javier; Paredes, Angel

2017-03-01

We numerically investigate spherically symmetric collapses in the Gross-Pitaevskii equation with attractive nonlinearity in a harmonic potential. Even below threshold for direct collapse, the wave function bounces off from the origin and may eventually become singular after a number of oscillations in the trapping potential. This is reminiscent of the evolution of Einstein gravity sourced by a scalar field in anti de Sitter space where collapse corresponds to black-hole formation. We carefully examine the long time evolution of the wave function for continuous families of initial states in order to sharpen out this qualitative coincidence which may bring new insights in both directions. On the one hand, we comment on possible implications for the so-called Bosenova collapses in cold atom Bose-Einstein condensates. On the other hand, Gross-Pitaevskii provides a toy model to study the relevance of either the resonance conditions or the nonlinearity for the problem of anti de Sitter instability.

Einstein, race, and the myth of the cultural icon

NASA Astrophysics Data System (ADS)

Jerome, Fred

2004-12-01

The most remarkable aspect of Einstein's 1946 address at Lincoln University is that it has vanished from Einstein's recorded history. Its disappearance into a historical black hole symbolizes what seems to happen in the creation of a cultural icon. It is but one of many political statements by Einstein to have met such a fate, though his civil rights activism is most glaringly mission. One explanation for this historical amnesia is that those who shape our official memories felt that Einstein's "controversial" friends like Paul Robeson and activities like co-chairing the anti-lynching crusade might tarnish Einstein as an icon. That icon, sanctified by Time magazine when it dubbed Einstein "Person of the Century" at the end of 1999, is a myth, albeit a marvelous one. Yet it is not so much the motive for the omission but the consequence of it that should concern us. Americans and the millions of Einstein fans around the world are left unaware that he was an outspoken, passionate, committed antiracist.

Einstein coefficients for rotational lines of the (0,0) band of the NO A2sigma(+)-X2Pi system

NASA Technical Reports Server (NTRS)

Reisel, John R.; Carter, Campbell D.; Laurendeau, Normand M.

1992-01-01

A summary of the spectroscopic equations necessary for prediction of the molecular transition energies and the Einstein A and B coefficients for rovibronic lines of the gamma(0,0) band of nitric oxide (NO) is presented. The calculated molecular transition energies are all within 0.57/cm of published experimental values; in addition, over 95 percent of the calculated energies give agreement with measured results within 0.25/cm. Einstein coefficients are calculated from the band A00 value and the known Hoenl-London factors and are tabulated for individual rovibronic transitions in the NO A2sigma(+)-X2Pi(0,0) band.

Observation of Two-Dimensional Localized Jones-Roberts Solitons in Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Meyer, Nadine; Proud, Harry; Perea-Ortiz, Marisa; O'Neale, Charlotte; Baumert, Mathis; Holynski, Michael; Kronjäger, Jochen; Barontini, Giovanni; Bongs, Kai

2017-10-01

Jones-Roberts solitons are the only known class of stable dark solitonic solutions of the nonlinear Schrödinger equation in two and three dimensions. They feature a distinctive elongated elliptical shape that allows them to travel without change of form. By imprinting a triangular phase pattern, we experimentally generate two-dimensional Jones-Roberts solitons in a three-dimensional atomic Bose-Einstein condensate. We monitor their dynamics, observing that this kind of soliton is indeed not affected by dynamic (snaking) or thermodynamic instabilities, that instead make other classes of dark solitons unstable in dimensions higher than one. Our results confirm the prediction that Jones-Roberts solitons are stable solutions of the nonlinear Schrödinger equation and promote them for applications beyond matter wave physics, like energy and information transport in noisy and inhomogeneous environments.

On static black holes solutions in Einstein and Einstein-Gauss-Bonnet gravity with topology [Formula: see text].

PubMed

Dadhich, Naresh; Pons, Josep M

We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet gravity with the topology of the product of two spheres, [Formula: see text], in higher dimensions. There is an unusual new feature of the Gauss-Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of [Formula: see text]. For an Einstein-Gauss-Bonnet black hole a limited window of negative values for [Formula: see text] is also permitted. This topology encompasses black strings, branes, and generalized Nariai metrics. We also give new solutions with the product of two spheres of constant curvature.

Non-Existence of Black Hole Solutionsfor a Spherically Symmetric, Static Einstein-Dirac-Maxwell System

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

We consider for j=1/2, 3/2,... a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein-Dirac-Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner-Nordstrom solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.

Einstein as a Missionary of Science

ERIC Educational Resources Information Center

Renn, Jürgen

2013-01-01

The paper reviews Einstein's engagement as a mediator and popularizer of science. It discusses the formative role of popular scientific literature for the young Einstein, showing that not only his broad scientific outlook but also his internationalist political views were shaped by these readings. Then, on the basis of recent detailed…

Exact ground-state correlation functions of an atomic-molecular Bose–Einstein condensate model

NASA Astrophysics Data System (ADS)

Links, Jon; Shen, Yibing

2018-05-01

We study the ground-state properties of an atomic-molecular Bose–Einstein condensate model through an exact Bethe Ansatz solution. For a certain range of parameter choices, we prove that the ground-state Bethe roots lie on the positive real-axis. We then use a continuum limit approach to obtain a singular integral equation characterising the distribution of these Bethe roots. Solving this equation leads to an analytic expression for the ground-state energy. The form of the expression is consistent with the existence of a line of quantum phase transitions, which has been identified in earlier studies. This line demarcates a molecular phase from a mixed phase. Certain correlation functions, which characterise these phases, are then obtained through the Hellmann–Feynman theorem.

Numerical investigations in the backflow region of a vacuum plume

NASA Technical Reports Server (NTRS)

Liaw, Goang-Shin

1992-01-01

The objective of this research is to numerically simulate the vacuum plume flow field in the backflow region of a low thrust nozzle exit. In space applications, the low thrust nozzles are used as a propulsion device to control the vehicle attitude, or to maneuver the vehicle flight trajectory. When the spacecraft is deployed in the orbit or cruising in a planetary mission, the vacuum plume is created behind the nozzle exit (so called backflow region), by the exhausting gas of the propulsion system or by venting internal gas to the extremely low density ambient. The low density vacuum plume flow regions cover the continuum, transitional and free molecular flow regimes, which were characterized by the Knudsen number K(sub n), K(sub n) = lambda(sub m)/L where lambda(sub m) is the mean free path of the gas molecules and L is the characteristic length of the flow field. The transitional regime is defined by 0.01 is less than or equal to K(sub n) is less than or equal to 10. The conventional Navier-Stokes equations are valid only in the flow region close to the nozzle exit since the validity of the Navier-Stokes equations fails asymptotically as the Knudsen number increases. The vacuum plume characteristics prediction is primarily a problem of transitional aerodynamics.

[The Einstein sign].

PubMed

Treska, V

2003-02-01

Untreated rupture of an aneurysm of the abdominal aorta is fatal in almost 100% of the patients. In the majority of cases the assessment of a correct, early diagnosis is simple (hypotension, backache, abdominal pain, pulsating resistance in the abdomen) and makes a prompt surgical or endovascular operation possible. In some instances however rupture of aneurysms of the abdominal aorta simulates other clinical conditions (acute cholecystitis, acute diverculitis of the sigmoid) which may delay the correct diagnosis and reduce the patient's chance of survival. The author describes, based on historical documents, the treacherous course of the disease in the scientific genius Albert Einstein where rupture of an aneurysm simulated acute cholecystitis, and in the world literature this symptomatology was subsequently described as Einstein's sign.

The NASA Beyond Einstein Program

NASA Technical Reports Server (NTRS)

White, Nicholas E.

2004-01-01

The Laser Interferometer Space Antenna (LISA) mission is part of NASA s Beyond Einstein program. This program seeks to answer the questions What Powered the Big Bang?, What happens at the edge of a Black Hole?, and What is Dark Energy?. LISA IS the first mission to be launched in this new program. This paper will give an overview of the Beyond Einstein program, its current status and where LISA fits in.

Modification of Einstein A Coefficient in Dissipative Gas Medium

NASA Technical Reports Server (NTRS)

Cao, Chang-Qi; Cao, Hui; Qin, Ke-Cheng

1996-01-01

Spontaneous radiation in dissipative gas medium such as plasmas is investigated by Langevin equations and the modified Weisskopf-Wigner approximation. Since the refractive index of gas medium is expected to be nearly unity, we shall first neglect the medium polarization effect. We show that absorption in plasmas may in certain case modify the Einstein A coefficient significantly and cause a pit in the A coefficient-density curves for relatively low temperature plasmas and also a pit in the A coefficient-temperature curves. In the next, the effect of medium polarization is taken into account in addition. To our surprise, its effect in certain case is quite significant. The dispersive curves show different behaviors in different region of parameters.

Topological Structures of Gravitational Vacuum as a Factor of Unclustered DM

NASA Astrophysics Data System (ADS)

Burdyuzha, V.; Pacheco, J.; Vereshkov, G.

2003-03-01

Topological structures of gravitational vacuum which could be produced in the result of the first relativistic phase transition or in the result of defect creation of the Universe from "nothing" are discussed. The concrete physical meaning is imparted to the parametrizational noninvariant members of Wheeler -DeWitt equation which may be considered as vacuum topological defects of different dimensions (worm-holes, micromembranes, microstrings and monopoles). After Universe inflation defects smoothed, stretches and broken up. They must be isotropic distributed on background of the expanding Universe. The part of them has survived and now they are perceiving as the structures of Λ -term, quintessence and unclustered dark matter. Mathematical illustration of these processes may be spontaneous breaking of global Lorentz-invariance of quantum geometrodynamics equations.

An exact solution for a thick domain wall in general relativity

NASA Technical Reports Server (NTRS)

Goetz, Guenter; Noetzold, Dirk

1989-01-01

An exact solution of the Einstein equations for a static, planar domain wall with finite thickness is presented. At infinity, density and pressure vanish and the space-time tends to the Minkowski vacuum on one side of the wall and to the Taub vacuum on the other side. A surprising feature of this solution is that the density and pressure distribution are symmetric about the central plane of the wall whereas the space-time metric and therefore also the gravitational field experienced by a test particle is asymmetric.

Onto the stability analysis of hyperbolic secant-shaped Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Sabari, S.; Murali, R.

2018-05-01

We analyze the stability of the hyperbolic secant-shaped attractive Bose-Einstein condensate in the absence of external trapping potential. The appropriate theoretical model for the system is described by the nonlinear mean-field Gross-Pitaevskii equation with time varying two-body interaction effects. Using the variational method, the stability of the system is analyzed under the influence of time varying two-body interactions. Further we confirm that the stability of the attractive condensate increases by considering the hyperbolic secant-shape profile instead of Gaussian shape. The analytical results are compared with the numerical simulation by employing the split-step Crank-Nicholson method.

How History Helped Einstein in Special Relativity

NASA Astrophysics Data System (ADS)

Martinez, Alberto

2013-04-01

I will discuss how the German intellectual movement known as ``critical history'' motivated several physicists in the late 1900s to radically analyze the fundamental principles of mechanics, leading eventually to Einstein's special theory of relativity. Eugen Karl Dühring, Johann Bernhard Stallo, Ludwig Lange, and Ernst Mach wrote critical histories of mechanics, some of which emphasized notions of relativity and observation, in opposition to old metaphysical concepts that seemed to infect the foundations of physics. This strand of critical history included the ``genetic method'' of analyzing how concepts develop over time, in our minds, by way of ordinary experiences, which by 1904 was young Albert Einstein's favorite approach for examining fundamental notions. Thus I will discuss how history contributed in Einstein's path to relativity, as well as comment more generally on Einstein's views on history.

Ferroelectricity by Bose-Einstein condensation in a quantum magnet.

PubMed

Kimura, S; Kakihata, K; Sawada, Y; Watanabe, K; Matsumoto, M; Hagiwara, M; Tanaka, H

2016-09-26

The Bose-Einstein condensation is a fascinating phenomenon, which results from quantum statistics for identical particles with an integer spin. Surprising properties, such as superfluidity, vortex quantization or Josephson effect, appear owing to the macroscopic quantum coherence, which spontaneously develops in Bose-Einstein condensates. Realization of Bose-Einstein condensation is not restricted in fluids like liquid helium, a superconducting phase of paired electrons in a metal and laser-cooled dilute alkali atoms. Bosonic quasi-particles like exciton-polariton and magnon in solids-state systems can also undergo Bose-Einstein condensation in certain conditions. Here, we report that the quantum coherence in Bose-Einstein condensate of the magnon quasi particles yields spontaneous electric polarization in the quantum magnet TlCuCl 3 , leading to remarkable magnetoelectric effect. Very soft ferroelectricity is realized as a consequence of the O(2) symmetry breaking by magnon Bose-Einstein condensation. The finding of this ferroelectricity will open a new window to explore multi-functionality of quantum magnets.

When champions meet: Rethinking the Bohr-Einstein debate

NASA Astrophysics Data System (ADS)

Landsman, N. P.

Einstein's philosophy of physics (as clarified by Fine, Howard, and Held) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws', to be impossible. Bohr's philosophy (as elucidated by Hooker, Scheibe, Folse, Howard, Held, and others), on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic quantum theory that-within an appropriate class of physical theories-suitable mathematical translations of the doctrines of Bohr and Einstein are equivalent. Thus-upon our specific formalization-quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted à la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in this constructive way, since their debate was dominated by Einstein's ingenious but ultimately flawed attempts to establish the "incompleteness" of quantum mechanics. This aspect of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein about the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, we can say that Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein's off-the-cuff characterization of Bohr as a 'Talmudic philosopher' was spot-on.

Vacuum-bag-only processing of composites

NASA Astrophysics Data System (ADS)

Thomas, Shad

Ultrasonic imaging in the C-scan mode in conjunction with the amplitude of the reflected signal was used to measure flow rates of an epoxy resin film penetrating through the thickness of single layers of woven carbon fabric. Assemblies, comprised of a single layer of fabric and film, were vacuum-bagged and ultrasonically scanned in a water tank during impregnation at 50°C, 60°C, 70°C, and 80°C. Measured flow rates were plotted versus inverse viscosity to determine the permeability in the thin film, non-saturated system. The results demonstrated that ultrasonic imaging in the C-scan mode is an effective method of measuring z-direction resin flow through a single layer of fabric. The permeability values determined in this work were consistent with permeability values reported in the literature. Capillary flow was not observed at the temperatures and times required for pressurized flow to occur. The flow rate at 65°C was predicted from the linear plot of flow rate versus inverse viscosity. The effects of fabric architecture on through-thickness flow rates during impregnation of an epoxy resin film were measured by ultrasonic imaging. Multilayered laminates comprised of woven carbon fabrics and epoxy films (prepregs) were fabricated by vacuum-bagging. Ultrasonic imaging was performed in a heated water tank (65°C) during impregnation. Impregnation rates showed a strong dependence on fabric architecture, despite similar areal densities. Impregnation rates are directly affected by inter-tow spacing and tow nesting, which depend on fabric architecture, and are indirectly affected by areal densities. A new method of predicting resin infusion rates in prepreg and resin film infusion processes was proposed. The Stokes equation was used to derive an equation to predict the impregnation rate of laminates as a function of fabric architecture. Flow rate data previously measured by ultrasound was analyzed with the new equation and the Kozeny-Carman equation. A fiber

Vacuum electron acceleration by coherent dipole radiation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Troha, A.L.; Van Meter, J.R.; Landahl, E.C.

1999-07-01

The validity of the concept of laser-driven vacuum acceleration has been questioned, based on an extrapolation of the well-known Lawson-Woodward theorem, which stipulates that plane electromagnetic waves cannot accelerate charged particles in vacuum. To formally demonstrate that electrons can indeed be accelerated in vacuum by focusing or diffracting electromagnetic waves, the interaction between a point charge and coherent dipole radiation is studied in detail. The corresponding four-potential exactly satisfies both Maxwell{close_quote}s equations and the Lorentz gauge condition everywhere, and is analytically tractable. It is found that in the far-field region, where the field distribution closely approximates that of a planemore » wave, we recover the Lawson-Woodward result, while net acceleration is obtained in the near-field region. The scaling of the energy gain with wave-front curvature and wave amplitude is studied systematically. {copyright} {ital 1999} {ital The American Physical Society}« less

Record bid for Einstein letter

NASA Astrophysics Data System (ADS)

Jeandron, Michelle

2008-06-01

A letter written by Albert Einstein the year before his death has sold for the staggering amount of £170 000 at an auction in London last month. The previously unrecorded letter, which has spent the past 50 years in a private collection, includes a discussion of Einstein's views on religion, bringing new material to the debate about whether or not he believed in God. The lot had been expected to fetch between £6000-£8000.

Vacuum force

NASA Astrophysics Data System (ADS)

Han, Yongquan

2015-03-01

To study on vacuum force, we must clear what is vacuum, vacuum is a space do not have any air and also ray. There is not exist an absolute the vacuum of space. The vacuum of space is relative, so that the vacuum force is relative. There is a certain that vacuum vacuum space exists. In fact, the vacuum space is relative, if the two spaces compared to the existence of relative vacuum, there must exist a vacuum force, and the direction of the vacuum force point to the vacuum region. Any object rotates and radiates. Rotate bend radiate- centripetal, gravity produced, relative gravity; non gravity is the vacuum force. Gravity is centripetal, is a trend that the objects who attracted wants to Centripetal, or have been do Centripetal movement. Any object moves, so gravity makes the object curve movement, that is to say, the radiation range curve movement must be in the gravitational objects, gravity must be existed in non vacuum region, and make the object who is in the region of do curve movement (for example: The earth moves around the sun), or final attracted in the form gravitational objects, and keep relatively static with attract object. (for example: objects on the earth moves but can't reach the first cosmic speed).

A comparative analysis of perspectives of Mileva Maric Einstein

NASA Astrophysics Data System (ADS)

Barnett, Carol C.

This dissertation examines the controversy surrounding Mileva Maric Einstein and the allegations subsequent to the publication of love letters during the time that Mileva Maric and Albert Einstein were students and during the early years of their marriage. It also examines the role of women in science from a historical perspective. Chapter One surveys the history of women in science from antiquity to the late nineteenth century and the patterns of gender related and restricting practices such as education, publication, the problem of mentoring and the issue of the lack of historical recognition. Chapter Two provides a comparative analyses between the lives of Mileva Maric Einstein and Marie Sklodowska Curie. Both had very similar social and educational backgrounds yet Marie Curie was able to work and publish jointly with her husband and received (although belatedly) international recognition for her work. On the other hand, Mileva Maric Einstein was never able to complete her degree and lived a life of obscurity and unfulfilled professional dreams. Both highly educated and intelligent women, but with drastically different outcomes in their professional and personal lives. Chapter Three examines the one book devoted to the life of Mileva Maric Einstein, Im Schatten Albert Einsteins: Das Tragische Leben der Mileva Einstein-Maric (In The Shadow of Albert Einstein: The Tragic Life of Mileva Maric), by Desanka Trbuhovic-Gjuric, Paul Haupt Publishers, 1985. It addresses the subjective as well as constructive and destructive criticisms of the various critical camps and provides examples of the statements made by the author which prompted a controversy within the academic and scientific communities. Appropriate responses are provided from various members of the scientific community to reflect the diversity of opinion and the intensity of the debate. Chapter Four addresses the problem of historicity and various interpretations of evidence which might suggest that the role

Self-gravitating static non-critical black holes in 4 D Einstein-Klein-Gordon system with nonminimal derivative coupling

NASA Astrophysics Data System (ADS)

Gunara, Bobby Eka; Yaqin, Ainol

2018-06-01

We study static non-critical hairy black holes of four dimensional gravitational model with nonminimal derivative coupling and a scalar potential turned on. By taking an ansatz, namely, the first derivative of the scalar field is proportional to square root of a metric function, we reduce the Einstein field equation and the scalar field equation of motions into a single highly nonlinear differential equation. This setup implies that the hair is secondary-like since the scalar charge-like depends on the non-constant mass-like quantity in the asymptotic limit. Then, we show that near boundaries the solution is not the critical point of the scalar potential and the effective geometries become spaces of constant scalar curvature.

BOOK REVIEW: The Legacy of Albert Einstein: A Collection of Essays in Celebration of the Year of Physics

NASA Astrophysics Data System (ADS)

Straumann, Norbert

2007-10-01

recent observational progress in cosmology and the emergence of the 'cosmic concordance model', with dark matter and dark energy as the dominant components of the current universe. Their discovery is widely considered as the most direct evidence for fundamental physics beyond the standard model of particle physics. In an introductory section Sarkar recalls the main reasons why the cosmological constant (vacuum energy) problem is of a very profound nature. In spite of some interesting ideas, no satisfactory solution is in sight. The article by B Sathyapakhash on gravitational radiation provides a readable introduction to the status of current detectors and astronomical sources of gravitational radiation. Of great cosmological interest are planned searches for a stochastic background of gravitational waves that is expected to have been produced by quantum processes in the very early universe. More than the first third of the book is devoted to current speculative attempts at creating a quantum theory of gravity, possibly within a unified coherent description of the known four fundamental interactions. Thanks to the enormously large value of the Planck energy in comparison to elementary particle masses, physicists may maintain for a long time, with success, a schizophrenic attitude in working within the framework of our present understanding, based on quantum field theory and classical general relativity. That physics cannot stay with that was already pointed out by Einstein in 1916, as A Ashtekar recalls in his essay. 'Einstein and the search for unification' by D Gross is the first article of the present book. In this he describes the reasons why, for those working in speculative areas, 'Einstein remains an inspiration for his foresight, and his unyielding determination and courage'. This inspiration is also manifest in the essays by M Atiyah, A Sen, and A Dabholkar on string theory. Hopefully, this book will find many readers, especially among graduate students, who can

Size-Dependent Materials Properties Toward a Universal Equation

PubMed Central

2010-01-01

Due to the lack of experimental values concerning some material properties at the nanoscale, it is interesting to evaluate this theoretically. Through a “top–down” approach, a universal equation is developed here which is particularly helpful when experiments are difficult to lead on a specific material property. It only requires the knowledge of the surface area to volume ratio of the nanomaterial, its size as well as the statistic (Fermi–Dirac or Bose–Einstein) followed by the particles involved in the considered material property. Comparison between different existing theoretical models and the proposed equation is done. PMID:20596422

Matter rogue waves in an F=1 spinor Bose-Einstein condensate.

PubMed

Qin, Zhenyun; Mu, Gui

2012-09-01

We report new types of matter rogue waves of a spinor (three-component) model of the Bose-Einstein condensate governed by a system of three nonlinearly coupled Gross-Pitaevskii equations. The exact first-order rational solutions containing one free parameter are obtained by means of a Darboux transformation for the integrable system where the mean-field interaction is attractive and the spin-exchange interaction is ferromagnetic. For different choices of the parameter, there exists a variety of different shaped solutions including two peaks in bright rogue waves and four dips in dark rogue waves. Furthermore, by utilizing the relation between the three-component and the one-component versions of the nonlinear Schrödinger equation, we can devise higher-order rational solutions, in which three components have different shapes. In addition, it is noteworthy that dark rogue wave features disappear in the third-order rational solution.

Einstein, Ethics and the Atomic Bomb

NASA Astrophysics Data System (ADS)

Rife, Patricia

2005-03-01

Einstein voiced his ethical views against war as well as fascism via venues and alliances with a variety of organizations still debated today. In 1939, he signed a letter to President Roosevelt (drafted by younger colleagues Szilard, Wigner and others) warning the U.S.government about the danger of Nazi Germany gaining control of uranium in the Belgian-controlled Congo in order to develop atomic weapons, based on the discovery of fission by Otto Hahn and Lise Meitner. In 1945, he became a member of the Princeton-based ``Emergency Committee for Atomic Scientists'' organized by Bethe, Condon, Bacher, Urey, Szilard and Weisskopf. Rare Einstein slides will illustrate Dr.Rife's presentation on Albert Einstein's philosophic and ethical convictions about peace, and public stance against war (1914-1950).

Quantum dynamics of a BEC interacting with a single-mode quantized field under the influence of a dissipation process: thermal and squeezed vacuum reservoirs

NASA Astrophysics Data System (ADS)

Ghasemian, E.; Tavassoly, M. K.

2017-09-01

In this paper we consider a system consisting of a number of two-level atoms in a Bose-Einstein condensate (BEC) and a single-mode quantized field, which interact with each other in the presence of two different damping sources, i.e. cavity and atomic reservoirs. The reservoirs which we consider here are thermal and squeezed vacuum ones corresponding to field and atom modes. Strictly speaking, by considering both types of reservoirs for each of the atom and field modes, we investigate the quantum dynamics of the interacting bosons in the system. Then, via solving the quantum Langevin equations for such a dissipative BEC system, we obtain analytical expressions for the time dependence of atomic population inversion, mean atom as well as photon number and quadrature squeezing in the field and atom modes. Our investigations demonstrate that for modeling the real physical systems, considering the dissipation effects is essential. Also, numerical calculations which are presented show that the atomic population inversion, the mean number of atoms in the BEC and the photons in the cavity possess damped oscillatory behavior due to the presence of reservoirs. In addition, non-classical squeezing effects in the field quadrature can be observed especially when squeezed vacuum reservoirs are taken into account. As an outstanding property of this model, we may refer to the fact that one can extract the atom-field coupling constant from the frequency of oscillations in the mentioned quantities such as atomic population inversion.

Controlling rogue waves in inhomogeneous Bose-Einstein condensates.

PubMed

Loomba, Shally; Kaur, Harleen; Gupta, Rama; Kumar, C N; Raju, Thokala Soloman

2014-05-01

We present the exact rogue wave solutions of the quasi-one-dimensional inhomogeneous Gross-Pitaevskii equation by using similarity transformation. Then, by employing the exact analytical solutions we have studied the controllable behavior of rogue waves in the Bose-Einstein condensates context for the experimentally relevant systems. Additionally, we have also investigated the nonlinear tunneling of rogue waves through a conventional hyperbolic barrier and periodic barrier. We have found that, for the conventional nonlinearity barrier case, rogue waves are localized in space and time and get amplified near the barrier, while for the dispersion barrier case rogue waves are localized in space and propagating in time and their amplitude is reduced at the barrier location. In the case of the periodic barrier, the interesting dynamical features of rogue waves are obtained and analyzed analytically.

Breathing Bright Solitons in a Bose Einstein Condensate

NASA Astrophysics Data System (ADS)

Chong, Gui-Shu; Hai, Wen-Hua; Xie, Qiong-Tao

2003-12-01

A Bose-Einstein condensate with time varying scattering length in time-dependent harmonic trap is analytically investigated and soliton-like solutions of the Gross-Pitaeviskii equation are obtained to describe single soliton, bisoliton and N-soliton properties of the matter wave. The influences of the geometrical property and modulate frequency of trapping potential on soliton behaviour are discussed. When the trap potential has a very small trap aspect ratio or oscillates with a high frequency, the matter wave preserves its shape nearly like a soliton train in propagation, while the breathing behaviour, which displays the periodic collapse and revival of the matter wave, is found for a relatively large aspect ratio or slow varying potential. Meanwhile mass centre of the matter wave translates and/or oscillates for different trap aspect ratio and trap frequencies.

Chaotic vortex filaments in a Bose–Einstein condensate and in superfluid helium

NASA Astrophysics Data System (ADS)

Nemirovskii, S. K.

2018-05-01

A statement of the quantum turbulence problem in both a Bose–Einstein condensate (BEC) and superfluid helium is formulated. In superfluid helium use is made of a so-called vortex filament method, in which quantum vortices are represented by stringlike objects, i.e. vortex lines. The dynamics of the vortex lines is determined by deterministic equations of motion, supplemented by random reconnections. Unlike He II, the laws of the dynamics of quantum vortices in BEC are based on the nonlinear Schrödinger equation. This makes it possible to obtain a microscopic description of the collision of vortices, the structure of a vortex filament, etc. A comparative analysis of these complementary approaches is carried out. It is shown that there are some features that do not automatically transfer the results obtained for BEC to vortices in He II and vice versa.

Einstein in Wyoming.

ERIC Educational Resources Information Center

Elliot, Ian

1996-01-01

Describes "Einstein's Adventurarium," a science center housed in an empty shopping mall in Gillette, Wyoming, created through school, business, and city-county government partnership. Describes how interactive exhibits allow exploration of life sciences, physics, and paleontology. (KDFB)

Quantum Mechanics of the Einstein-Hopf Model.

ERIC Educational Resources Information Center

Milonni, P. W.

1981-01-01

The Einstein-Hopf model for the thermodynamic equilibrium between the electromagnetic field and dipole oscillators is considered within the framework of quantum mechanics. Both the wave and particle aspects of the Einstein fluctuation formula are interpreted in terms of the fundamental absorption and emission processes. (Author/SK)

Stationary and moving solitons in spin-orbit-coupled spin-1 Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Li, Yu-E.; Xue, Ju-Kui

2018-04-01

We investigate the matter-wave solitons in a spin-orbit-coupled spin-1 Bose-Einstein condensate using a multiscale perturbation method. Beginning with the one-dimensional spin-orbit-coupled threecomponent Gross-Pitaevskii equations, we derive a single nonlinear Schrödinger equation, which allows determination of the analytical soliton solutions of the system. Stationary and moving solitons in the system are derived. In particular, a parameter space for different existing soliton types is provided. It is shown that there exist only dark or bright solitons when the spin-orbit coupling is weak, with the solitons depending on the atomic interactions. However, when the spin-orbit coupling is strong, both dark and bright solitons exist, being determined by the Raman coupling. Our analytical solutions are confirmed by direct numerical simulations.

Collapsing spherical star in Scalar-Einstein-Gauss-Bonnet gravity with a quadratic coupling

NASA Astrophysics Data System (ADS)

Chakrabarti, Soumya

2018-04-01

We study the evolution of a self interacting scalar field in Einstein-Gauss-Bonnet theory in four dimension where the scalar field couples non minimally with the Gauss-Bonnet term. Considering a polynomial coupling of the scalar field with the Gauss-Bonnet term, a self-interaction potential and an additional perfect fluid distribution alongwith the scalar field, we investigate different possibilities regarding the outcome of the collapsing scalar field. The strength of the coupling and choice of the self-interaction potential serves as the pivotal initial conditions of the models presented. The high degree of non-linearity in the equation system is taken care off by using a method of invertibe point transformation of anharmonic oscillator equation, which has proven itself very useful in recent past while investigating dynamics of minimally coupled scalar fields.

Motion of vortices in inhomogeneous Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Groszek, Andrew J.; Paganin, David M.; Helmerson, Kristian; Simula, Tapio P.

2018-02-01

We derive a general and exact equation of motion for a quantized vortex in an inhomogeneous two-dimensional Bose-Einstein condensate. This equation expresses the velocity of a vortex as a sum of local ambient density and phase gradients in the vicinity of the vortex. We perform Gross-Pitaevskii simulations of single-vortex dynamics in both harmonic and hard-walled disk-shaped traps, and find excellent agreement in both cases with our analytical prediction. The simulations reveal that, in a harmonic trap, the main contribution to the vortex velocity is an induced ambient phase gradient, a finding that contradicts the commonly quoted result that the local density gradient is the only relevant effect in this scenario. We use our analytical vortex velocity formula to derive a point-vortex model that accounts for both density and phase contributions to the vortex velocity, suitable for use in inhomogeneous condensates. Although good agreement is obtained between Gross-Pitaevskii and point-vortex simulations for specific few-vortex configurations, the effects of nonuniform condensate density are in general highly nontrivial, and are thus difficult to efficiently and accurately model using a simplified point-vortex description.

What about Albert Einstein? Using Biographies to Promote Students' Scientific Thinking

ERIC Educational Resources Information Center

Fingon, Joan C.; Fingon, Shallon D.

2009-01-01

Who hasn't heard of Einstein? Science educators everywhere are familiar with Einstein's genius and general theory of relativity. Students easily recognize Einstein's image by his white flyaway hair and bushy mustache. It is well known that Einstein was a brilliant physicist and an abstract thinker who often used his creativity and imagination in…

QED multi-dimensional vacuum polarization finite-difference solver

NASA Astrophysics Data System (ADS)

Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo

2015-11-01

The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph

Competition between Bose-Einstein Condensation and Spin Dynamics.

PubMed

Naylor, B; Brewczyk, M; Gajda, M; Gorceix, O; Maréchal, E; Vernac, L; Laburthe-Tolra, B

2016-10-28

We study the impact of spin-exchange collisions on the dynamics of Bose-Einstein condensation by rapidly cooling a chromium multicomponent Bose gas. Despite relatively strong spin-dependent interactions, the critical temperature for Bose-Einstein condensation is reached before the spin degrees of freedom fully thermalize. The increase in density due to Bose-Einstein condensation then triggers spin dynamics, hampering the formation of condensates in spin-excited states. Small metastable spinor condensates are, nevertheless, produced, and they manifest in strong spin fluctuations.

Einstein's Mirror

ERIC Educational Resources Information Center

Gjurchinovski, Aleksandar; Skeparovski, Aleksandar

2008-01-01

Reflection of light from a plane mirror in uniform rectilinear motion is a century-old problem, intimately related to the foundations of special relativity. The problem was first investigated by Einstein in his famous 1905 paper by using the Lorentz transformations to switch from the mirror's rest frame to the frame where the mirror moves at a…

Einstein Revisited

ERIC Educational Resources Information Center

Fine, Leonard

2005-01-01

A brief description on the work and life of the great physicist scientist Albert Einstein is presented. The photoelectric paper written by him in 1905 led him to the study of fluctuations in the energy density of radiation and from there to the incomplete nature of the equipartition theorem of classical mechanics, which failed to account for…

Modeling of Water Injection into a Vacuum

NASA Technical Reports Server (NTRS)

Alred, John W.; Smith, Nicole L.; Wang, K. C.; Lumpkin, Forrest E.; Fitzgerald, Steven M.

1997-01-01

A loosely coupled two-phase vacuum water plume model has been developed. This model consists of a source flow model to describe the expansion of water vapor, and the Lagrangian equations of motion for particle trajectories. Gas/Particle interaction is modeled through the drag force induced by the relative velocities. Particles are assumed traveling along streamlines. The equations of motion are integrated to obtain particle velocity along the streamline. This model has been used to predict the mass flux in a 5 meter radius hemispherical domain resulting from the burst of a water jet of 1.5 mm in diameter, mass flow rate of 24.2 g/s, and stagnation pressure of 21.0 psia, which is the nominal Orbiter water dump condition. The result is compared with an empirical water plume model deduced from a video image of the STS-29 water dump. To further improve the model, work has begun to numerically simulate the bubble formation and bursting present in a liquid stream injected into a vacuum. The technique of smoothed particle hydrodynamics was used to formulate this simulation. A status and results of the on-going effort are presented and compared to results from the literature.

Stability of thin shell wormholes with a modified Chaplygin gas in Einstein-Hoffman-Born-Infeld theory

NASA Astrophysics Data System (ADS)

Eid, A.

2017-11-01

In the framework of Darmois-Israel formalism, the dynamics of motion equations of spherically symmetric thin shell wormholes that are supported by a modified Chaplygin gas in Einstein-Hoffman-Born-Infeld theory are constructed. The stability analysis of a thin shell wormhole is also discussed using a linearized radial perturbation around static solutions at the wormhole throat. The existence of stable static solutions depends on the value of some parameters of dynamical shell.

Relativistic Bose-Einstein condensates thin-shell wormholes

NASA Astrophysics Data System (ADS)

Richarte, M. G.; Salako, I. G.; Graça, J. P. Morais; Moradpour, H.; Övgün, Ali

2017-10-01

We construct traversable thin-shell wormholes which are asymptotically Ads/dS applying the cut and paste procedure for the case of an acoustic metric created by a relativistic Bose-Einstein condensate. We examine several definitions of the flare-out condition along with the violation or not of the energy conditions for such relativistic geometries. Under reasonable assumptions about the equation of state of the matter located at the shell, we concentrate on the mechanical stability of wormholes under radial perturbation preserving the original spherical symmetry. To do so, we consider linearized perturbations around static solutions. We obtain that dS acoustic wormholes remain stable under radial perturbations as long as they have small radius; such wormholes with finite radius do not violate the strong/null energy condition. Besides, we show that stable Ads wormhole satisfy some of the energy conditions whereas unstable Ads wormhole with large radii violate them.

Criteria for genuine N -partite continuous-variable entanglement and Einstein-Podolsky-Rosen steering

NASA Astrophysics Data System (ADS)

Teh, R. Y.; Reid, M. D.

2014-12-01

Following previous work, we distinguish between genuine N -partite entanglement and full N -partite inseparability. Accordingly, we derive criteria to detect genuine multipartite entanglement using continuous-variable (position and momentum) measurements. Our criteria are similar but different to those based on the van Loock-Furusawa inequalities, which detect full N -partite inseparability. We explain how the criteria can be used to detect the genuine N -partite entanglement of continuous variable states generated from squeezed and vacuum state inputs, including the continuous-variable Greenberger-Horne-Zeilinger state, with explicit predictions for up to N =9 . This makes our work accessible to experiment. For N =3 , we also present criteria for tripartite Einstein-Podolsky-Rosen (EPR) steering. These criteria provide a means to demonstrate a genuine three-party EPR paradox, in which any single party is steerable by the remaining two parties.

Stochastic modification of the Schrödinger-Newton equation

NASA Astrophysics Data System (ADS)

Bera, Sayantani; Mohan, Ravi; Singh, Tejinder P.

2015-07-01

The Schrödinger-Newton (SN) equation describes the effect of self-gravity on the evolution of a quantum system, and it has been proposed that gravitationally induced decoherence drives the system to one of the stationary solutions of the SN equation. However, the equation itself lacks a decoherence mechanism, because it does not possess any stochastic feature. In the present work we derive a stochastic modification of the Schrödinger-Newton equation, starting from the Einstein-Langevin equation in the theory of stochastic semiclassical gravity. We specialize this equation to the case of a single massive point particle, and by using Karolyhazy's phase variance method, we derive the Diósi-Penrose criterion for the decoherence time. We obtain a (nonlinear) master equation corresponding to this stochastic SN equation. This equation is, however, linear at the level of the approximation we use to prove decoherence; hence, the no-signaling requirement is met. Lastly, we use physical arguments to obtain expressions for the decoherence length of extended objects.

Black-hole universe: time evolution.

PubMed

Yoo, Chul-Moon; Okawa, Hirotada; Nakao, Ken-ichi

2013-10-18

Time evolution of a black hole lattice toy model universe is simulated. The vacuum Einstein equations in a cubic box with a black hole at the origin are numerically solved with periodic boundary conditions on all pairs of faces opposite to each other. Defining effective scale factors by using the area of a surface and the length of an edge of the cubic box, we compare them with that in the Einstein-de Sitter universe. It is found that the behavior of the effective scale factors is well approximated by that in the Einstein-de Sitter universe. In our model, if the box size is sufficiently larger than the horizon radius, local inhomogeneities do not significantly affect the global expansion law of the Universe even though the inhomogeneity is extremely nonlinear.

Covariant Formulation of Fluid Dynamics and Estakhr's Material Geodesic Equation, far down the Rabbit hole

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2013-11-01

``When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein'' You probably will not need to ask these questions of God, I've already answered both of them. Uμ = γ (c , u (r --> , t)) denotes four-velocity field. Jμ = ρUμ denotes four-current mass density. Estakhr's Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. DJμ/Dτ =dJμ/Dτ +ΓαβμJαUβ =JνΩμν +∂νTμν +ΓαβμJαUβ Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is DJμ/Dτ =JνFμν +∂νTμν +ΓαβμJαUβ electromagnetism.

Einstein's Years in Switzerland

NASA Astrophysics Data System (ADS)

Plendl, Hans S.

2005-11-01

Albert Einstein left Germany, the country of his birth, in 1894 and moved to Switzerland in 1895. He studied, worked and taught there, except for a year's stay in Prague, until1914. That year he returned to Germany, where he lived until his emigration to the United States in 1933. In 1905, while living with his wife Mileva and their first son Hans Albert in Bern and working as a technical expert at the Swiss Patent Office, he published his dissertation on the determination of molecular dimensions, his papers on Brownian Motion that helped to establish the Kinetic Theory of Heat and on the Photo-Electric Effect that validated the Quantum Theory of Light, and the two papers introducing the Special Theory of Relativity. How the young Einstein could help to lay the foundations of these theories while still working on his dissertation, holding a full-time job and helping to raise a family has evoked much discussion among his biographers. In this contribution, the extent to which living within Swiss society and culture could have made this feat possible will be examined. Old and recent photos of places in Switzerland where Einstein has lived and worked will be shown.

What Einstein Can Teach Us about Education

ERIC Educational Resources Information Center

Hayes, Denis

2007-01-01

People are more likely to associate Einstein with complex scientific theories and mathematical calculations than with education theory. In fact, Einstein's own experiences of schooling and his reflections on the meaning of life and the significance of education are profound and oddly relevant to the situation that pertains in England today. It is…

From Einstein's theorem to Bell's theorem: a history of quantum non-locality

NASA Astrophysics Data System (ADS)

Wiseman, H. M.

2006-04-01

In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.

Derivation of Einstein-Cartan theory from general relativity

NASA Astrophysics Data System (ADS)

Petti, Richard

2015-04-01

General relativity cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. Einstein-Cartan theory fixes this problem in the least invasive way. In the late 20th century, the consensus view was that Einstein-Cartan theory requires inclusion of torsion without adequate justification, it has no empirical support (though it doesn't conflict with any known evidence), it solves no important problem, and it complicates gravitational theory with no compensating benefit. In 1986 the author published a derivation of Einstein-Cartan theory from general relativity, with no additional assumptions or parameters. Starting without torsion, Poincaré symmetry, classical or quantum spin, or spinors, it derives torsion and its relation to spin from a continuum limit of general relativistic solutions. The present work makes the case that this computation, combined with supporting arguments, constitutes a derivation of Einstein-Cartan theory from general relativity, not just a plausibility argument. This paper adds more and simpler explanations, more computational details, correction of a factor of 2, discussion of limitations of the derivation, and discussion of some areas of gravitational research where Einstein-Cartan theory is relevant.

Post-Planck constraints on interacting vacuum energy

NASA Astrophysics Data System (ADS)

Wang, Yuting; Wands, David; Zhao, Gong-Bo; Xu, Lixin

2014-07-01

We present improved constraints on an interacting vacuum model using updated astronomical observations including the first data release from Planck. We consider a model with one dimensionless parameter, α, describing the interaction between dark matter and vacuum energy (with fixed equation of state w=-1). The background dynamics correspond to a generalized Chaplygin gas cosmology, but the perturbations have a zero sound speed. The tension between the value of the Hubble constant, H0, determined by Planck data plus WMAP polarization (Planck +WP) and that determined by the Hubble Space Telescope (HST) can be alleviated by energy transfer from dark matter to vacuum (α>0). A positive α increases the allowed values of H0 due to parameter degeneracy within the model using only cosmic microwave background data. Combining with additional data sets of including supernova type Ia (SN Ia) and baryon acoustic oscillation (BAO), we can significantly tighten the bounds on α. Redshift-space distortions (RSD), which constrain the linear growth of structure, provide the tightest constraints on vacuum interaction when combined with Planck+WP, and prefer energy transfer from vacuum to dark matter (α<0) which suppresses the growth of structure. Using the combined data sets of Planck +WP+Union2.1+BAO+RSD, we obtain the constraint on α to be -0.083<α<-0.006 (95% C.L.), allowing low H0 consistent with the measurement from 6dF Galaxy survey. This interacting vacuum model can alleviate the tension between RSD and Planck +WP in the ΛCDM model for α <0, or between HST measurements of H0 and Planck+WP for α>0, but not both at the same time.

Einsteins Spuren in den Archiven der Wissenschaft: Physikgeschichte

NASA Astrophysics Data System (ADS)

Marx, Werner

2005-07-01

Die Erwähnungen und Zitierungen von Einsteins Arbeiten dokumentieren lediglich den quantifizierbaren Anteil von Einsteins Beitrag zur Physik. Gleichwohl belegen sie die außergewöhnliche Resonanz und Langzeitwirkung seiner Arbeiten. Die Häufigkeit der Zitierungen entspricht nicht der allgemeinen Einschätzung ihrer Bedeutung. Insbesondere die Pionierarbeiten werden inzwischen als bekannt vorausgesetzt und nicht mehr explizit zitiert. Interessanterweise ist seine nach 1945 meist zitierte Arbeit nicht eine der Pionierarbeiten zur Quantenphysik oder Relativitätstheorie, sondern jene aus dem Jahr 1935 zum berühmten Einstein-Podolsky-Rosen-Paradoxon.

[Photoeffects, Einstein's light quanta and the history of their acceptance].

PubMed

Wiederkehr, Karl Heinrich

2006-01-01

It is generally supposed, that the discovery of the efficacy-quantum by Planck was the impetus to Einstein's hypothesis of lightquanta. With its help Einstein could explain the external light-electrical effect. But even years before Einstein had worked at the photoeffect and already made experiments on it. For that reason the article gives a short survey about the history of the lightelectric effects. Lenard's basical work about the release of the photoelectrons is dealt with in detail, without which Einstein would scarcely have found his lightquanta. Furthermore it is shown how difficult it was for the physicists to give up--at least partially--the traditional view of the undulation-nature of light, and how they searched to explain the great energies of the photoelectrons. On the other side it is set forth how Einstein's formula of lightquanta was gradually confirmed. The tragical development of Einstein's personal relations with Johannes Stark and Philipp Lenard are briefly described. Stark was one of the few who supported Einstein's ideas at the beginning. Only with the Compton-effect, which could only be quantitatively interpreted by means of lightquanta and the special theory of relativity 1923, the way was free for the general acceptance of the lightquanta. Einstein did not agree to the obtained dualism of undulation and corpuscle; he had a different solution in mind about the fusion of the two forms of appearance of light.

Direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation.

PubMed

Garcia, Alejandro L; Wagner, Wolfgang

2003-11-01

In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.

Compact setup for the production of {sup 87}Rb |F = 2, m{sub F} = + 2〉 Bose-Einstein condensates in a hybrid trap

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nolli, Raffaele; Venturelli, Michela; Marmugi, Luca, E-mail: l.marmugi@ucl.ac.uk

We present a compact experimental apparatus for Bose-Einstein condensation of {sup 87}Rb in the |F  =  2, m{sub F} = + 2〉 state. A pre-cooled atomic beam of {sup 87}Rb is obtained by using an unbalanced magneto-optical trap, allowing controlled transfer of trapped atoms from the first vacuum chamber to the science chamber. Here, atoms are transferred to a hybrid trap, as produced by overlapping a magnetic quadrupole trap with a far-detuned optical trap with crossed beam configuration, where forced radiofrequency evaporation is realized. The final evaporation leading to Bose-Einstein condensation is then performed by exponentially lowering the optical trapmore » depth. Control and stabilization systems of the optical trap beams are discussed in detail. The setup reliably produces a pure condensate in the |F = 2, m{sub F} = + 2〉 state in 50 s, which includes 33 s loading of the science magneto-optical trap and 17 s forced evaporation.« less

Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Fadel, Matteo; Zibold, Tilman; Décamps, Boris; Treutlein, Philipp

2018-04-01

Many-particle entanglement is a fundamental concept of quantum physics that still presents conceptual challenges. Although nonclassical states of atomic ensembles were used to enhance measurement precision in quantum metrology, the notion of entanglement in these systems was debated because the correlations among the indistinguishable atoms were witnessed by collective measurements only. Here, we use high-resolution imaging to directly measure the spin correlations between spatially separated parts of a spin-squeezed Bose-Einstein condensate. We observe entanglement that is strong enough for Einstein-Podolsky-Rosen steering: We can predict measurement outcomes for noncommuting observables in one spatial region on the basis of corresponding measurements in another region with an inferred uncertainty product below the Heisenberg uncertainty bound. This method could be exploited for entanglement-enhanced imaging of electromagnetic field distributions and quantum information tasks.

Decay of the de Sitter vacuum

NASA Astrophysics Data System (ADS)

Anderson, Paul R.; Mottola, Emil; Sanders, Dillon H.

2018-03-01

The decay rate of the Bunch-Davies state of a massive scalar field in the expanding flat spatial sections of de Sitter space is determined by an analysis of the particle pair creation process in real time. The Feynman definition of particle and antiparticle Fourier mode solutions of the scalar wave equation and their adiabatic phase analytically continued to the complexified time domain show conclusively that the Bunch-Davies state is not the vacuum state at late times. The closely analogous creation of charged particle pairs in a uniform electric field is reviewed and Schwinger's result for the vacuum decay rate is recovered by this same real time analysis. The vacuum decay rate in each case is also calculated by switching the background field on adiabatically, allowing it to act for a very long time, and then adiabatically switching it off again. In both the uniform electric field and de Sitter cases, the particles created while the field is switched on are verified to be real, in the sense that they persist in the final asymptotic flat zero-field region. In the de Sitter case, there is an interesting residual dependence of the rate on how the de Sitter phase is ended, indicating a greater sensitivity to spatial boundary conditions. The electric current of the created particles in the E -field case and their energy density and pressure in the de Sitter case are also computed, and the magnitude of their backreaction effects on the background field estimated. Possible consequences of the Hubble scale instability of the de Sitter vacuum for cosmology, vacuum dark energy, and the cosmological "constant" problem are discussed.

EPR before EPR: A 1930 Einstein-Bohr thought Experiment Revisited

ERIC Educational Resources Information Center

Nikolic, Hrvoje

2012-01-01

In 1930, Einstein argued against the consistency of the time-energy uncertainty relation by discussing a thought experiment involving a measurement of the mass of the box which emitted a photon. Bohr seemingly prevailed over Einstein by arguing that Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit…

The Langevin equation

NASA Astrophysics Data System (ADS)

Pomeau, Yves; Piasecki, Jarosław

2017-11-01

The existence of atoms has been long predicted by philosophers and scientists. The development of thermodynamics and of the statistical interpretation of its concepts at the end of the nineteenth century and in the early years of the twentieth century made it possible to bridge the gap of scales between the macroscopic world and the world of atoms. Einstein and Smoluchowski showed in 1905 and 1906 that the Brownian motion of particles of measurable size is a manifestation of the motion of atoms in fluids. Their derivation was completely different from each other. Langevin showed in 1908 how to put in a coherent framework the subtle effect of the randomness of the atomic world, responsible for the fluctuating force driving the motion of the Brownian particle and the viscosity of the "macroscopic" flow taking place around the same Brownian particle. Whereas viscous forces were already well understood at this time, the "Langevin" force appears there for the first time: it represents the fluctuating part of the interaction between the Brownian particle and the surrounding fluid. We discuss the derivation by Einstein and Smoluchowski as well as a previous paper by Sutherland on the diffusion coefficient of large spheres. Next we present Langevin's short note and explain the fundamental splitting into a random force and a macroscopic viscous force. This brings us to discuss various points, like the kind of constraints on Langevin-like equations. We insist in particular on the one arising from the time-reversal symmetry of the equilibrium fluctuations. Moreover, we discuss another constraint, raised first by Lorentz, which implies that, if the Brownian particle is not very heavy, the viscous force cannot be taken as the standard Stokes drag on an object moving at uniform speed. Lastly, we examine the so-called Langevin-Heisenberg and/or Langevin-Schrödinger equation used in quantum mechanics.

The Stokes-Einstein relation at moderate Schmidt number.

PubMed

Balboa Usabiaga, Florencio; Xie, Xiaoyi; Delgado-Buscalioni, Rafael; Donev, Aleksandar

2013-12-07

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently developed minimally resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The mismatch arises because thermal fluctuations affect the drag coefficient for a particle due to the nonlinear nature of the fluid-particle coupling. The numerical data are in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.

New Information about Albert Einstein's Brain.

PubMed

Falk, Dean

2009-01-01

In order to glean information about hominin (or other) brains that no longer exist, details of external neuroanatomy that are reproduced on endocranial casts (endocasts) from fossilized braincases may be described and interpreted. Despite being, of necessity, speculative, such studies can be very informative when conducted in light of the literature on comparative neuroanatomy, paleontology, and functional imaging studies. Albert Einstein's brain no longer exists in an intact state, but there are photographs of it in various views. Applying techniques developed from paleoanthropology, previously unrecognized details of external neuroanatomy are identified on these photographs. This information should be of interest to paleoneurologists, comparative neuroanatomists, historians of science, and cognitive neuroscientists. The new identifications of cortical features should also be archived for future scholars who will have access to additional information from improved functional imaging technology. Meanwhile, to the extent possible, Einstein's cerebral cortex is investigated in light of available data about variation in human sulcal patterns. Although much of his cortical surface was unremarkable, regions in and near Einstein's primary somatosensory and motor cortices were unusual. It is possible that these atypical aspects of Einstein's cerebral cortex were related to the difficulty with which he acquired language, his preference for thinking in sensory impressions including visual images rather than words, and his early training on the violin.

Gravitational vacuum condensate stars.

PubMed

Mazur, Pawel O; Mottola, Emil

2004-06-29

A new final state of gravitational collapse is proposed. By extending the concept of Bose-Einstein condensation to gravitational systems, a cold, dark, compact object with an interior de Sitter condensate p(v) = -rho(v) and an exterior Schwarzschild geometry of arbitrary total mass M is constructed. These regions are separated by a shell with a small but finite proper thickness l of fluid with equation of state p = +rho, replacing both the Schwarzschild and de Sitter classical horizons. The new solution has no singularities, no event horizons, and a global time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of the order k(B)lMc/Planck's over 2 pi, instead of the Bekenstein-Hawking entropy formula, S(BH) = 4 pi k(B)GM(2)/Planck's over 2 pi c. Hence, unlike black holes, the new solution is thermodynamically stable and has no information paradox.

Bose-Einstein condensation. Twenty years after

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bagnato, V. S.; Frantzeskakis, D. J.; Kevrekidis, P. G.

The aim of this introductory article is two-fold. First, we aim to offer a general introduction to the theme of Bose-Einstein condensates, and briefly discuss the evolution of a number of relevant research directions during the last two decades. Second, we introduce and present the articles that appear in this Special Volume of Romanian Reports in Physics celebrating the conclusion of the second decade since the experimental creation of Bose-Einstein condensation in ultracold gases of alkali-metal atoms.

Bose-Einstein condensation. Twenty years after

DOE PAGES

Bagnato, V. S.; Frantzeskakis, D. J.; Kevrekidis, P. G.; ...

2015-02-23

The aim of this introductory article is two-fold. First, we aim to offer a general introduction to the theme of Bose-Einstein condensates, and briefly discuss the evolution of a number of relevant research directions during the last two decades. Second, we introduce and present the articles that appear in this Special Volume of Romanian Reports in Physics celebrating the conclusion of the second decade since the experimental creation of Bose-Einstein condensation in ultracold gases of alkali-metal atoms.

Some Exact Solutions of a Nonintegrable Toda-type Equation

NASA Astrophysics Data System (ADS)

Kim, Chanju

2018-05-01

We study a Toda-type equation with two scalar fields which is not integrable and construct two families of exact solutions which are expressed in terms of rational functions. The equation appears in U(1) Chern-Simons theories coupled to two nonrelativistic matter fields with opposite charges. One family of solutions is a trivial embedding of Liouville-type solutions. The other family is obtained by transforming the equation into the Taubes vortex equation on the hyperbolic space. Though the Taubes equation is not integrable, a trivial vacuum solution provides nontrivial solutions to the original Toda-type equation.

Geometry of the submanifolds of SEXn. II. The generalized fundamental equations for the hypersubmanifold of SEXn

NASA Astrophysics Data System (ADS)

Chung, Kyung Tae; Lee, Jong Woo

1989-08-01

A connection which is both Einstein and semisymmetric is called an SE connection, and a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by g λμ through an SE connection is called an n-dimensional SE manifold and denoted by SEXn. This paper is a direct continuation of earlier work. In this paper, we derive the generalized fundamental equations for the hypersubmanifold of SEXn, including generalized Gauss formulas, generalized Weingarten equations, and generalized Gauss-Codazzi equations.

Can a supersonically expanding Bose-Einstein Condensates be used to study cosmological inflation?

NASA Astrophysics Data System (ADS)

Banik, Swarnav; Eckel, Stephen; Kumar, Avinash; Jacobson, Ted; Spielman, Ian; Campbell, Gretchen

2017-04-01

The massive scale of the universe makes the experimental study of cosmological inflation difficult. This has led to an interest in developing analogous systems using table top experiments. Here, we present the basic features of an expanding universe by drawing parallels with an expanding toroidal Bose Einstein Condensate (BEC) of 23Na atoms. The toroidal BEC serves as the background vacuum and phonons are the analogue to photons in the expanding universe. We study the dynamics of phonons in both non-expanding and expanding condensates and measure dissipation using the structure factor. We demonstrate red shifting of phonons and quasi-particle production similar to pre-heating after the inflation of universe. At the end of expansion, we also observe spontaneous non-zero winding numbers in the ring. Using Monte-Carlo simulations, we predict the widths of the resulting winding number distribution, which agree well with our experimental findings.

Reassessing the Ritz-Einstein debate on the radiation asymmetry in classical electrodynamics

NASA Astrophysics Data System (ADS)

Frisch, Mathias; Pietsch, Wolfgang

2016-08-01

We investigate the debate between Walter Ritz and Albert Einstein on the origin and nature of the radiation asymmetry. We argue that Ritz's views on the radiation asymmetry were far richer and nuanced than the oft-cited joint letter with Einstein (Ritz & Einstein, 1909) suggests, and that Einstein's views in 1909 on the asymmetry are far more ambiguous than is commonly recognized. Indeed, there is strong evidence that Einstein ultimately came to agree with Ritz that elementary radiation processes in classical electrodynamics are non-symmetric and fully retarded.

Einstein, Bohr, and Bell

NASA Astrophysics Data System (ADS)

Bellac, Michel Le

2014-11-01

The final form of quantum physics, in the particular case of wave mechanics, was established in the years 1925-1927 by Heisenberg, Schrödinger, Born and others, but the synthesis was the work of Bohr who gave an epistemological interpretation of all the technicalities built up over those years; this interpretation will be examined briefly in Chapter 10. Although Einstein acknowledged the success of quantum mechanics in atomic, molecular and solid state physics, he disagreed deeply with Bohr's interpretation. For many years, he tried to find flaws in the formulation of quantum theory as it had been more or less accepted by a large majority of physicists, but his objections were brushed away by Bohr. However, in an article published in 1935 with Podolsky and Rosen, universally known under the acronym EPR, Einstein thought he had identified a difficulty in the by then standard interpretation. Bohr's obscure, and in part beyond the point, answer showed that Einstein had hit a sensitive target. Nevertheless, until 1964, the so-called Bohr-Einstein debate stayed uniquely on a philosophical level, and it was actually forgotten by most physicists, as the few of them aware of it thought it had no practical implication. In 1964, the Northern Irish physicist John Bell realized that the assumptions contained in the EPR article could be tested experimentally. These assumptions led to inequalities, the Bell inequalities, which were in contradiction with quantum mechanical predictions: as we shall see later on, it is extremely likely that the assumptions of the EPR article are not consistent with experiment, which, on the contrary, vindicates the predictions of quantum physics. In Section 3.2, the origin of Bell's inequalities will be explained with an intuitive example, then they will be compared with the predictions of quantum theory in Section 3.3, and finally their experimental status will be reviewed in Section 3.4. The debate between Bohr and Einstein goes much beyond a

Head-on collision of ring dark solitons in Bose Einstein condensates

NASA Astrophysics Data System (ADS)

Xue, Ju-Kui; Peng, Ping

2006-06-01

The ring dark solitons and their head-on collisions in a Bose-Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincaré-Lighthill-Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r-1/3 law and depend on the initial soliton amplitude and radius.

Global Resolution of the Physical Vacuum Singularity for Three-Dimensional Isentropic Inviscid Flows with Damping in Spherically Symmetric Motions

NASA Astrophysics Data System (ADS)

Zeng, Huihui

2017-10-01

For the gas-vacuum interface problem with physical singularity and the sound speed being {C^{{1}/{2}}}-Hölder continuous near vacuum boundaries of the isentropic compressible Euler equations with damping, the global existence of smooth solutions and the convergence to Barenblatt self-similar solutions of the corresponding porous media equation are proved in this paper for spherically symmetric motions in three dimensions; this is done by overcoming the analytical difficulties caused by the coordinate's singularity near the center of symmetry, and the physical vacuum singularity to which standard methods of symmetric hyperbolic systems do not apply. Various weights are identified to resolve the singularity near the vacuum boundary and the center of symmetry globally in time. The results obtained here contribute to the theory of global solutions to vacuum boundary problems of compressible inviscid fluids, for which the currently available results are mainly for the local-in-time well-posedness theory, and also to the theory of global smooth solutions of dissipative hyperbolic systems which fail to be strictly hyperbolic.

Vacuum thin shells in Einstein–Gauss–Bonnet brane-world cosmology

NASA Astrophysics Data System (ADS)

Ramirez, Marcos A.

2018-04-01

In this paper we construct new solutions of the Einstein–Gauss–Bonnet field equations in an isotropic Shiromizu–Maeda–Sasaki brane-world setting which represent a couple of Z 2-symmetric vacuum thin shells splitting from the central brane, and explore the main properties of the dynamics of the system. The matching of the separating vacuum shells with the brane-world is as smooth as possible and all matter fields are restricted to the brane. We prove the existence of these solutions, derive the criteria for their existence, analyse some fundamental aspects or their evolution and demonstrate the possibility of constructing cosmological examples that exhibit this feature at early times. We also comment on the possible implications for cosmology and the relation of this system with the thermodynamic instability of highly symmetric vacuum solutions of Lovelock theory.

Indian Vacuum Society: The Indian Vacuum Society

NASA Astrophysics Data System (ADS)

Saha, T. K.

2008-03-01

The Indian Vacuum Society (IVS) was established in 1970. It has over 800 members including many from Industry and R & D Institutions spread throughout India. The society has an active chapter at Kolkata. The society was formed with the main aim to promote, encourage and develop the growth of Vacuum Science, Techniques and Applications in India. In order to achieve this aim it has conducted a number of short term courses at graduate and technician levels on vacuum science and technology on topics ranging from low vacuum to ultrahigh vacuum So far it has conducted 39 such courses at different parts of the country and imparted training to more than 1200 persons in the field. Some of these courses were in-plant training courses conducted on the premises of the establishment and designed to take care of the special needs of the establishment. IVS also regularly conducts national and international seminars and symposia on vacuum science and technology with special emphasis on some theme related to applications of vacuum. A large number of delegates from all over India take part in the deliberations of such seminars and symposia and present their work. IVS also arranges technical visits to different industries and research institutes. The society also helped in the UNESCO sponsored post-graduate level courses in vacuum science, technology and applications conducted by Mumbai University. The society has also designed a certificate and diploma course for graduate level students studying vacuum science and technology and has submitted a syllabus to the academic council of the University of Mumbai for their approval, we hope that some colleges affiliated to the university will start this course from the coming academic year. IVS extended its support in standardizing many of the vacuum instruments and played a vital role in helping to set up a Regional Testing Centre along with BARC. As part of the development of vacuum education, the society arranges the participation of

The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

NASA Technical Reports Server (NTRS)

Hoots, F. R.; Fitzpatrick, P. M.

1979-01-01

The classical Poisson equations of rotational motion are used to study the attitude motions of an earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the earth. A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Long-term solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.

Castles in the Air: The Einstein-De Sitter Debate, 1916-1918

NASA Astrophysics Data System (ADS)

Midwinter, Charles; Janssen, Michel

2011-03-01

The Einstein De Sitter debate marked the birth of modern cosmology and the infamous cosmological constant. For Einstein, the controversy was essentially a philosophical one. Einstein's insistence on a static Universe and Mach's Principle guided him in the construction of his own cosmological model, and compelled him to criticize De Sitter's. For De Sitter, the debate began as idle conjecture. Before long, however, he began to wonder if the "spacious castles" he and Einstein had constructed might actually represent physical reality. We plan to write a volume that reproduces the documents relevant to the debate. Our commentary will retrace and explain the arguments of the historical players, complete with calculations. For the first time readers will be able to follow the arguments of Einstein and De Sitter in a detailed exploration of the first two relativistic cosmological models. Readers will see how Einstein's flawed criticisms of De Sitter were supported by Herman Weyl, and finally how Felix Klein settled the whole matter with a coordinate transformation.

Beyond Einstein: Exploring the Extreme Universe

NASA Technical Reports Server (NTRS)

Barbier, Louis M.

2005-01-01

This paper will give an overview of the NASA Universe Division Beyond Einstein program. The Beyond Einstein program consists of a series of exploratory missions to investigate some of the most important and pressing problems in modern-day astrophysics - including searches for Dark Energy and studies of the earliest times in the universe, during the inflationary period after the Big Bang. A variety of new technologies are being developed both in the science instrumentation these missions will carry and in the spacecraft that will carry those instruments.

Stochastic quantization of (λϕ4)d scalar theory: Generalized Langevin equation with memory kernel

NASA Astrophysics Data System (ADS)

Menezes, G.; Svaiter, N. F.

2007-02-01

The method of stochastic quantization for a scalar field theory is reviewed. A brief survey for the case of self-interacting scalar field, implementing the stochastic perturbation theory up to the one-loop level, is presented. Then, it is introduced a colored random noise in the Einstein's relations, a common prescription employed by one of the stochastic regularizations, to control the ultraviolet divergences of the theory. This formalism is extended to the case where a Langevin equation with a memory kernel is used. It is shown that, maintaining the Einstein's relations with a colored noise, there is convergence to a non-regularized theory.

Renormalization of Einstein gravity through a derivative-dependent field redefinition

NASA Astrophysics Data System (ADS)

Slovick, Brian

2018-01-01

This work explores an alternative solution to the problem of renormalizability in Einstein gravity. In the proposed approach, Einstein gravity is transformed into the renormalizable theory of four-derivative gravity by applying a local field redefinition containing an infinite number of higher derivatives. It is also shown that the current-current amplitude is invariant with the field redefinition, and thus the unitarity of Einstein gravity is preserved.

Covariant Formulation of Fluid Dynamics and Estakhr's Material Geodesic Equation, far down the Rabbit hole

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2012-07-01

``When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein'' You probably will not need to ask these questions of God, I've already answered both of them. U^{μ}=γ (c,u({r}, t)) denotes four-velocity field. J^ {μ}=ρ U^{μ} denotes four-current mass density. Estakhr's Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. {DJ^ {μ}}/{Dτ}={dJ^{μ}}/{D τ}+Γ^{μ}_{α β}J^{α}U^{β}=J_ {ν}Ω^{μν}+npartial_ {ν}T^{μν}+Γ^{μ} _{αβ}J^{α}U^{β} Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is {DJ^ {μ}}/{Dτ}=J_{ν}F^{μν} +partial_{ν}T^{μν}+ Γ^{μ}_{αβ}J^ {α}U^{β} electromagnetism.

Einstein's First Steps Toward General Relativity: Gedanken Experiments and Axiomatics

NASA Astrophysics Data System (ADS)

Miller, A. I.

1999-03-01

Albert Einstein's 1907 Jahrbuch paper is an extraordinary document because it contains his first steps toward generalizing the 1905 relativity theory to include gravitation. Ignoring the apparent experimental disconfirmation of the 1905 relativity theory and his unsuccessful attempts to generalize the mass-energy equivalence, Einstein boldly raises the mass-energy equivalence to an axiom, invokes equality between gravitational and inertial masses, and then postulates the equivalence between a uniform gravitational field and an oppositely directed constant acceleration, the equivalence principle. How did this come about? What is at issue is scientific creativity. This necessitates broadening historical analysis to include aspects of cognitive science such as the role of visual imagery in Einstein's thinking, and the relation between conscious and unconscious modes of thought in problem solving. This method reveals the catalysts that sparked a Gedanken experiment that occurred to Einstein while working on the Jahrbuch paper. A mental model is presented to further explore Einstein's profound scientific discovery.

Spacetime-bridge solutions in vacuum gravity

NASA Astrophysics Data System (ADS)

Sengupta, Sandipan

2017-11-01

Vacuum spacetime solutions, which are representations of a bridgelike geometry, are constructed as purely geometric sources of curvature in gravity theory. These configurations satisfy the first-order equations of motion everywhere. Each of them consists of two identical sheets of asymptotically flat geometry, connected by a region of finite extension where the tetrad is noninvertible. The solutions can be classified into nonstatic and static spacetimes. The first class represents a single causal universe equipped (locally) with a timelike coordinate everywhere. The latter, on the other hand, could be interpreted as a sum of two self-contained universes which are causally disconnected. These geometries, even though they have different metrical dimensions in the regions within and away from the bridge, are regular. This is reflected through the associated gauge-covariant fields, which are continuous across the hypersurfaces connecting the invertible and noninvertible phases of the tetrad and are finite everywhere. These vacuum bridge solutions have no analogue in the Einsteinian theory of gravity.

Einstein's Jury -The Race to Test Relativity

NASA Astrophysics Data System (ADS)

Crelinsten, Jeffrey

2006-12-01

It is common belief that Einstein’s general theory of relativity won worldwide acceptance after British astronomers announced in November 1919 that the sun’s gravitational field bends starlight by an amount predicted by Einstein. This paper demonstrates that the case for Einstein was not settled until much later and that there was considerable confusion and debate about relativity during this period. Most astronomers considered Einstein’s general theory too metaphysical and abstruse, and many tried to find more conventional explanations of the astronomical observations. Two American announcements before the British results appeared had been contrary to Einstein’s prediction. They came from Lick and Mt. Wilson observatories, which enjoyed international reputations as two of the most advanced astrophysical research establishments in the world. Astronomers at these renowned institutions were instrumental in swaying the court of scientific opinion during the decade of the 1920s, which saw numerous attempts to measure light-bending, as well as solar line displacements and even ether-drift. How astronomers approached the “Einstein problem” in these early years before and after the First World War, and how the public reacted to what they reported, helped to shape attitudes we hold today about Einstein and his ideas.

Einstein's 1917 static model of the universe: a centennial review

NASA Astrophysics Data System (ADS)

O'Raifeartaigh, Cormac; O'Keeffe, Michael; Nahm, Werner; Mitton, Simon

2017-08-01

We present a historical review of Einstein's 1917 paper ` Cosmological Considerations in the General Theory of Relativity' to mark the centenary of a key work that set the foundations of modern cosmology. We find that the paper followed as a natural next step after Einstein's development of the general theory of relativity and that the work offers many insights into his thoughts on relativity, astronomy and cosmology. Our review includes a description of the observational and theoretical background to the paper; a paragraph-by-paragraph guided tour of the work; a discussion of Einstein's views of issues such as the relativity of inertia, the curvature of space and the cosmological constant. Particular attention is paid to little-known aspects of the paper such as Einstein's failure to test his model against observation, his failure to consider the stability of the model and a mathematical oversight concerning his interpretation of the role of the cosmological constant. We recall the response of theorists and astronomers to Einstein's cosmology in the context of the alternate models of the universe proposed by Willem de Sitter, Alexander Friedman and Georges Lemaître. Finally, we consider the relevance of the Einstein World in today's `emergent' cosmologies.

Solitons and rogue waves in spinor Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Li, Sitai; Prinari, Barbara; Biondini, Gino

2018-02-01

We present a general classification of one-soliton solutions as well as families of rogue-wave solutions for F =1 spinor Bose-Einstein condensates (BECs). These solutions are obtained from the inverse scattering transform for a focusing matrix nonlinear Schrödinger equation which models condensates in the case of attractive mean-field interactions and ferromagnetic spin-exchange interactions. In particular, we show that when no background is present, all one-soliton solutions are reducible via unitary transformations to a combination of oppositely polarized solitonic solutions of single-component BECs. On the other hand, we show that when a nonzero background is present, not all matrix one-soliton solutions are reducible to a simple combination of scalar solutions. Finally, by taking suitable limits of all the solutions on a nonzero background we also obtain three families of rogue-wave (i.e., rational) solutions.

Solitons and rogue waves in spinor Bose-Einstein condensates.

PubMed

Li, Sitai; Prinari, Barbara; Biondini, Gino

2018-02-01

We present a general classification of one-soliton solutions as well as families of rogue-wave solutions for F=1 spinor Bose-Einstein condensates (BECs). These solutions are obtained from the inverse scattering transform for a focusing matrix nonlinear Schrödinger equation which models condensates in the case of attractive mean-field interactions and ferromagnetic spin-exchange interactions. In particular, we show that when no background is present, all one-soliton solutions are reducible via unitary transformations to a combination of oppositely polarized solitonic solutions of single-component BECs. On the other hand, we show that when a nonzero background is present, not all matrix one-soliton solutions are reducible to a simple combination of scalar solutions. Finally, by taking suitable limits of all the solutions on a nonzero background we also obtain three families of rogue-wave (i.e., rational) solutions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiménez, Jose Beltrán; Heisenberg, Lavinia; Olmo, Gonzalo J., E-mail: jose.beltran@uclouvain.be, E-mail: Lavinia.Heisenberg@unige.ch, E-mail: gonzalo.olmo@csic.es

We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a minimal version of the theory, for which we study solutions in the presence of a perfect fluid with special attention to the cosmological evolution. Inmore » vacuum we recover Ricci-flat solutions, but also an additional physical solution corresponding to an Einstein space. The existence of two physical branches remains for non-vacuum solutions and, in addition, the branch that connects to the Einstein space in vacuum is not very sensitive to the specific value of the energy density. For the branch that connects to the General Relativity limit we generically find three behaviours for the Hubble function depending on the equation of state of the fluid, namely: either there is a maximum value for the energy density that connects continuously with vacuum, or the energy density can be arbitrarily large but the Hubble function saturates and remains constant at high energy densities, or the energy density is unbounded and the Hubble function grows faster than in General Relativity. The second case is particularly interesting because it could offer an interesting inflationary epoch even in the presence of a dust component. Finally, we discuss the possibility of avoiding certain types of singularities within the minimal model.« less

Infrared lessons for ultraviolet gravity: the case of massive gravity and Born-Infeld

NASA Astrophysics Data System (ADS)

Beltrán Jiménez, Jose; Heisenberg, Lavinia; Olmo, Gonzalo J.

2014-11-01

We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a minimal version of the theory, for which we study solutions in the presence of a perfect fluid with special attention to the cosmological evolution. In vacuum we recover Ricci-flat solutions, but also an additional physical solution corresponding to an Einstein space. The existence of two physical branches remains for non-vacuum solutions and, in addition, the branch that connects to the Einstein space in vacuum is not very sensitive to the specific value of the energy density. For the branch that connects to the General Relativity limit we generically find three behaviours for the Hubble function depending on the equation of state of the fluid, namely: either there is a maximum value for the energy density that connects continuously with vacuum, or the energy density can be arbitrarily large but the Hubble function saturates and remains constant at high energy densities, or the energy density is unbounded and the Hubble function grows faster than in General Relativity. The second case is particularly interesting because it could offer an interesting inflationary epoch even in the presence of a dust component. Finally, we discuss the possibility of avoiding certain types of singularities within the minimal model.

(2+1)-Dimensional charged black holes with scalar hair in Einstein-Power-Maxwell Theory

NASA Astrophysics Data System (ADS)

Xu, Wei; Zou, De-Cheng

2017-06-01

In (2+1)-dimensional AdS spacetime, we obtain new exact black hole solutions, including two different models (power parameter k=1 and k≠1), in the Einstein-Power-Maxwell (EPM) theory with nonminimally coupled scalar field. For the charged hairy black hole with k≠1, we find that the solution contains a curvature singularity at the origin and is nonconformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Later, the null geodesic equations for photon around this charged hairy black hole are also discussed in detail.

Stripes and honeycomb lattice of quantized vortices in rotating two-component Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Kasamatsu, Kenichi; Sakashita, Kouhei

2018-05-01

We study numerically the structure of a vortex lattice in rotating two-component Bose-Einstein condensates with equal atomic masses and equal intra- and intercomponent coupling strengths. The numerical simulations of the Gross-Pitaevskii equation show that the quantized vortices in this situation form lattice configuration accompanying vortex stripes, honeycomb lattices, and their complexes. This is a result of the degeneracy of the system for the SU(2) symmetric operation, which causes a continuous transformation between the above structures. In terms of the pseudospin representation, the complex lattice structures are identified as a hexagonal lattice of doubly winding half skyrmions.

Coherence, Abstraction, and Personal Involvement: Albert Einstein, Physicist and Humanist.

ERIC Educational Resources Information Center

Ne'eman, Yuval

1979-01-01

Reviews Einstein's main contributions to physics, and analyzes the importance of a coherent body of theory. Einstein's involvement in nonscientific issues such as nuclear disarmament is also included. (HM)

In the limelight of stars. Einstein, Mandl, and the origins of gravitational lens research (German Title: Im Rampenlicht der Sterne. Einstein, Mandl und die Ursprünge der Gravitationslinsenforschung)

NASA Astrophysics Data System (ADS)

Renn, Jürgen; Sauer, Tilman

Einstein's paper on gravitational lensing from 1936 was published only as a result of insistent prodding by the Czech amateur scientist Rudi Mandl. We discuss Mandl's role for the publication history of Einstein's paper and point out striking similarities between Mandl's situation in 1936 and Einstein's own position in 1912. At that time, Einstein himself had already considered the idea of gravitational lensing, as had been discovered some years ago through the identification of research notes from that period. Other early discussions of gravitational lensing by Lodge, Chwolson, Tikhov, Zwicky, Russell, and others were either only perceived or only written after Mandl had succeeded to persuade Einstein into publication.

Franz Selety (1893-1933?). His cosmological investigations and the correspondence with Einstein (German Title: Franz Selety (1893-1933?). Seine kosmologischen Arbeiten und der Briefwechsel mit Einstein)

NASA Astrophysics Data System (ADS)

Jung, Tobias

In 1922, Franz Selety, university-bred philosopher and self-educated physicist and cosmologist, developed a molecular hierarchical, spatially infinite, Newtonian cosmological model. His considerations were based on his earlier philosophical work published in 1914 as well as on the early correspondence with Einstein in 1917. Historically, the roots of hierarchical models can be seen in 18th century investigations by Thomas Wright of Durham, Immanuel Kant and Johann Heinrich Lambert. Those investigations were taken up by Edmund Fournier d'Albe and Carl Charlier at the beginning of the 20th century. Selety's cosmological model was criticized by Einstein mainly due to its spatial infiniteness which in Einstein's opinion seemed to contradict Mach's principle. This criticism sheds light on Einstein's conviction that with his first cosmological model, namely the static, spatially infinite, though unbounded Einstein Universe of 1917, the appropriate cosmological theory already had been established.

Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in Bose-Einstein condensates.

PubMed

Fadel, Matteo; Zibold, Tilman; Décamps, Boris; Treutlein, Philipp

2018-04-27

Many-particle entanglement is a fundamental concept of quantum physics that still presents conceptual challenges. Although nonclassical states of atomic ensembles were used to enhance measurement precision in quantum metrology, the notion of entanglement in these systems was debated because the correlations among the indistinguishable atoms were witnessed by collective measurements only. Here, we use high-resolution imaging to directly measure the spin correlations between spatially separated parts of a spin-squeezed Bose-Einstein condensate. We observe entanglement that is strong enough for Einstein-Podolsky-Rosen steering: We can predict measurement outcomes for noncommuting observables in one spatial region on the basis of corresponding measurements in another region with an inferred uncertainty product below the Heisenberg uncertainty bound. This method could be exploited for entanglement-enhanced imaging of electromagnetic field distributions and quantum information tasks. Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.

Explaining Electromagnetic Plane Waves in a Vacuum at the Introductory Level

ERIC Educational Resources Information Center

Allred, Clark L.; Della-Rose, Devin J.; Flusche, Brian M.; Kiziah, Rex R.; Lee, David J.

2010-01-01

A typical introduction to electromagnetic waves in vacuum is illustrated by the following quote from an introductory physics text: "Maxwell's equations predict that an electromagnetic wave consists of oscillating electric and magnetic fields. The changing fields induce each other, which maintains the propagation of the wave; a changing electric…

Albert Einstein and his mentor Max Talmey. The seventh Charles B. Snyder Lecture.

PubMed

Ravin, J G

1997-01-01

While he was a student at the Munich medical school, Max Talmey strongly influenced the education of Albert Einstein. Their association occurred during five years of Einstein's second decade. They lost contact for many years after each left Munich. Talmey emigrated to the United States and practiced medicine, mainly ophthalmology, in New York City. He made significant contributions to medicine, to the popularization of Einstein's work, and to the development of international languages. The relationship of Talmey and Einstein was rekindled when Einstein visited and later moved to the United States.

Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers

NASA Astrophysics Data System (ADS)

Nyman, Robert A.; Walker, Benjamin T.

2018-03-01

Photons can come to thermal equilibrium at room temperature by scattering multiple times from a fluorescent dye. By confining the light and dye in a microcavity, a minimum energy is set and the photons can then show Bose-Einstein condensation. We present here the physical principles underlying photon thermalization and condensation, and review the literature on the subject. We then explore the 'small' regime where very few photons are needed for condensation. We compare thermal equilibrium results to a rate-equation model of microlasers, which includes spontaneous emission into the cavity, and we note that small systems result in ambiguity in the definition of threshold.

From Newton to Einstein.

ERIC Educational Resources Information Center

Ryder, L. H.

1987-01-01

Discusses the history of scientific thought in terms of the theories of inertia and absolute space, relativity and gravitation. Describes how Sir Isaac Newton used the work of earlier scholars in his theories and how Albert Einstein used Newton's theories in his. (CW)

Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

NASA Astrophysics Data System (ADS)

Muruganandam, P.; Adhikari, S. K.

2009-10-01

Here we develop simple numerical algorithms for both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation describing the properties of Bose-Einstein condensates at ultra low temperatures. In particular, we consider algorithms involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method. In a one-space-variable form of the GP equation we consider the one-dimensional, two-dimensional circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. Numerical results for the chemical potential and root-mean-square size of stationary states are reported using imaginary-time propagation programs for all the cases and compared with previously obtained results. Also presented are numerical results of non-stationary oscillation for different trap symmetries using real-time propagation programs. A set of convenient working codes developed in Fortran 77 are also provided for all these cases (twelve programs in all). In the case of two or three space variables, Fortran 90/95 versions provide some simplification over the Fortran 77 programs, and these programs are also included (six programs in all). Program summaryProgram title: (i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial Catalogue identifier: AEDU_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data

Nonequilibrium Bose-Einstein condensation of hot magnons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vannucchi, Fabio Stucchi; Vasconcellos, Aurea Rosas; Luzzi, Roberto

We present an analysis of the emergence of a nonequilibrium Bose-Einstein-type condensation of magnons in radio-frequency pumped magnetic thin films, which has recently been experimentally observed. A complete description of all the nonequilibrium processes involved is given. It is demonstrated that the phenomenon is another example of the emergence of Bose-Einstein-type condensation in nonequilibrium many-boson systems embedded in a thermal bath, a phenomenon evidenced decades ago by the renowned late Herbert Froehlich.

q-deformed Einstein's model to describe specific heat of solid

NASA Astrophysics Data System (ADS)

Guha, Atanu; Das, Prasanta Kumar

2018-04-01

Realistic phenomena can be described more appropriately using generalized canonical ensemble, with proper parameter sets involved. We have generalized the Einstein's theory for specific heat of solid in Tsallis statistics, where the temperature fluctuation is introduced into the theory via the fluctuation parameter q. At low temperature the Einstein's curve of the specific heat in the nonextensive Tsallis scenario exactly lies on the experimental data points. Consequently this q-modified Einstein's curve is found to be overlapping with the one predicted by Debye. Considering only the temperature fluctuation effect(even without considering more than one mode of vibration is being triggered) we found that the CV vs T curve is as good as obtained by considering the different modes of vibration as suggested by Debye. Generalizing the Einstein's theory in Tsallis statistics we found that a unique value of the Einstein temperature θE along with a temperature dependent deformation parameter q(T) , can well describe the phenomena of specific heat of solid i.e. the theory is equivalent to Debye's theory with a temperature dependent θD.

On thermionic emission and the use of vacuum tubes in the advanced physics laboratory

NASA Astrophysics Data System (ADS)

Angiolillo, Paul J.

2009-12-01

Two methods are outlined for measuring the charge-to-mass ratio e /me of the electron using thermionic emission as exploited in vacuum tube technology. One method employs the notion of the space charge in the vacuum tube diode as described by the Child-Langmuir equation; the other method uses the electron trajectories in vacuum tube pentodes with cylindrical electrodes under conditions of orthogonally related electric and magnetic fields (the Hull magnetron method). The vacuum diode method gave e /me=1.782±0.166×10+11 C/kg (averaged over the vacuum diodes studied), and the Hull magnetron method gave e /me=1.779±0.208×10+11 C/kg (averaged over both pentodes and the anode voltages studied). These methods afford opportunities for students to determine the e /me ratio without using the Bainbridge tube method and to become familiar with phenomena not normally covered in a typical experimental methods curriculum.

Vacuum mechatronics

NASA Technical Reports Server (NTRS)

Hackwood, Susan; Belinski, Steven E.; Beni, Gerardo

1989-01-01

The discipline of vacuum mechatronics is defined as the design and development of vacuum-compatible computer-controlled mechanisms for manipulating, sensing and testing in a vacuum environment. The importance of vacuum mechatronics is growing with an increased application of vacuum in space studies and in manufacturing for material processing, medicine, microelectronics, emission studies, lyophylisation, freeze drying and packaging. The quickly developing field of vacuum mechatronics will also be the driving force for the realization of an advanced era of totally enclosed clean manufacturing cells. High technology manufacturing has increasingly demanding requirements for precision manipulation, in situ process monitoring and contamination-free environments. To remove the contamination problems associated with human workers, the tendency in many manufacturing processes is to move towards total automation. This will become a requirement in the near future for e.g., microelectronics manufacturing. Automation in ultra-clean manufacturing environments is evolving into the concept of self-contained and fully enclosed manufacturing. A Self Contained Automated Robotic Factory (SCARF) is being developed as a flexible research facility for totally enclosed manufacturing. The construction and successful operation of a SCARF will provide a novel, flexible, self-contained, clean, vacuum manufacturing environment. SCARF also requires very high reliability and intelligent control. The trends in vacuum mechatronics and some of the key research issues are reviewed.

Kantowski-Sachs Einstein-æther perfect fluid models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Latta, Joey; Leon, Genly; Paliathanasis, Andronikos, E-mail: lattaj@mathstat.dal.ca, E-mail: genly.leon@pucv.cl, E-mail: anpaliat@phys.uoa.gr

We investigate Kantowski-Sachs models in Einstein-æ ther theory with a perfect fluid source using the singularity analysis to prove the integrability of the field equations and dynamical system tools to study the evolution. We find an inflationary source at early times, and an inflationary sink at late times, for a wide region in the parameter space. The results by A.A. Coley, G. Leon, P. Sandin and J. Latta ( JCAP 12 (2015) 010), are then re-obtained as particular cases. Additionally, we select other values for the non-GR parameters which are consistent with current constraints, getting a very rich phenomenology. Inmore » particular, we find solutions with infinite shear, zero curvature, and infinite matter energy density in comparison with the Hubble scalar. We also have stiff-like future attractors, anisotropic late-time attractors, or both, in some special cases. Such results are developed analytically, and then verified by numerics. Finally, the physical interpretation of the new critical points is discussed.« less

Going Beyond Einstein with the Constellation-X Mission

NASA Technical Reports Server (NTRS)

White, Nicholas

2007-01-01

The Constellation-X mission will address the questions: "What happens to matter close to a black hole?" and "What is Dark Energy?" These questions are central to the NASA Beyond Einstein Program, where Constellation-X plays a central role. The mission will address these questions by using high throughput X-ray spectroscopy to observe the effects of strong gravity close to the event horizon of black holes, and to observe the formation and evolution of clusters of galaxies in order to precisely determine Cosmological parameters. To achieve these primary science goals requires a factor of 25-100 increase in sensitivity for high resolution X-ray spectroscopy.'The mission will also perform routine high-resolution X-ray spectroscopy of faint 2nd extended X-ray source populations. This will provide diagnostic information such as density, elemental abundances, velocity; and ionization state for a wide range of astrophysical problems, including new constraints on the Neutron Star equation of state.

Atom loss resonances in a Bose-Einstein condensate.

PubMed

Langmack, Christian; Smith, D Hudson; Braaten, Eric

2013-07-12

Atom loss resonances in ultracold trapped atoms have been observed at scattering lengths near atom-dimer resonances, at which Efimov trimers cross the atom-dimer threshold, and near two-dimer resonances, at which universal tetramers cross the dimer-dimer threshold. We propose a new mechanism for these loss resonances in a Bose-Einstein condensate of atoms. As the scattering length is ramped to the large final value at which the atom loss rate is measured, the time-dependent scattering length generates a small condensate of shallow dimers coherently from the atom condensate. The coexisting atom and dimer condensates can be described by a low-energy effective field theory with universal coefficients that are determined by matching exact results from few-body physics. The classical field equations for the atom and dimer condensates predict narrow enhancements in the atom loss rate near atom-dimer resonances and near two-dimer resonances due to inelastic dimer collisions.

Einstein-Podolsky-Rosen entanglement and steering in two-well Bose-Einstein-condensate ground states

NASA Astrophysics Data System (ADS)

He, Q. Y.; Drummond, P. D.; Olsen, M. K.; Reid, M. D.

2012-08-01

We consider how to generate and detect Einstein-Podolsky-Rosen (EPR) entanglement and the steering paradox between groups of atoms in two separated potential wells in a Bose-Einstein condensate. We present experimental criteria for this form of entanglement and propose experimental strategies for detecting entanglement using two- or four-mode ground states. These approaches use spatial and/or internal modes. We also present higher-order criteria that act as signatures to detect the multiparticle entanglement present in this system. We point out the difference between spatial entanglement using separated detectors and other types of entanglement that do not require spatial separation. The four-mode approach with two spatial and two internal modes results in an entanglement signature with spatially separated detectors, conceptually similar to the original EPR paradox.

Einstein's Biggest Blunder: A Cosmic Mystery Story

ScienceCinema

Krauss, Lawrence

2018-01-11

The standard model of cosmology built up over 20 years is no longer accepted as accurate. New data suggest that most of the energy density of the universe may be contained in empty space. Remarkably, this is exactly what would be expected if Einstein's cosmological constant really exists. If it does, its origin is the biggest mystery in physics and presents huge challenges for the fundamental theories of elementary particles and fields. Krauss explains Einstein's concept and describes its possible implications.

Compliance of the Stokes-Einstein model and breakdown of the Stokes-Einstein-Debye model for a urea-based supramolecular polymer of high viscosity.

PubMed

Świergiel, Jolanta; Bouteiller, Laurent; Jadżyn, Jan

2014-11-14

Impedance spectroscopy was used for the study of the static and dynamic behavior of the electrical conductivity of a hydrogen-bonded supramolecular polymer of high viscosity. The experimental data are discussed in the frame of the Stokes-Einstein and Stokes-Einstein-Debye models. It was found that the translational movement of the ions is due to normal Brownian diffusion, which was revealed by a fulfillment of Ohm's law by the electric current and a strictly exponential decay of the current after removing the electric stimulus. The dependence of the dc conductivity on the viscosity of the medium fulfills the Stokes-Einstein model quite well. An extension of the model, by including in it the conductivity relaxation time, is proposed in this paper. A breakdown of the Stokes-Einstein-Debye model is revealed by the relations of the dipolar relaxation time to the viscosity and to the dc ionic conductivity. The importance of the C=O···H-N hydrogen bonds in that breakdown is discussed.

Natural vacuum electronics

NASA Technical Reports Server (NTRS)

Leggett, Nickolaus

1990-01-01

The ambient natural vacuum of space is proposed as a basis for electron valves. Each valve is an electron controlling structure similiar to a vacuum tube that is operated without a vacuum sustaining envelope. The natural vacuum electron valves discussed offer a viable substitute for solid state devices. The natural vacuum valve is highly resistant to ionizing radiation, system generated electromagnetic pulse, current transients, and direct exposure to space conditions.

Generalized Bose-Einstein Condensation in Superconductivity

NASA Astrophysics Data System (ADS)

de Llano, Manuel

2011-03-01

Unification of the BCS and the Bose-Einstein condensation (BEC) theories is surveyed in detail via a generalized BEC (GBEC) finite-temperature statistical formalism. Its major difference with BCS theory is that it can be diagonalized exactly. Under specified conditions it yields the precise BCS gap equation for all temperatures as well as the precise BCS zero-temperature condensation energy for all couplings, thereby suggesting that a BCS condensate is a BE condensate in a ternary mixture of kinematically independent unpaired electrons coexisting with equally proportioned weakly-bound two-electron and two-hole Cooper pairs. Without abandoning the electron-phonon mechanism in moderately weak coupling it suffices, in principle, to reproduce the unusually high values of Tc (in units of the Fermi temperature TF) of 0.01-0.05 empirically reported in the so-called "exotic" superconductors of the Uemura plot, including cuprates, in contrast to the low values of Tc/TF ≤ 10-3 roughly reproduced by BCS theory for conventional (mostly elemental) superconductors. Replacing the characteristic phonon-exchange Debye temperature by a characteristic magnon-exchange one more than twice in size can lead to a simple interaction model associated with spin-fluctuation-mediated pairing.

Generalized Bose-Einstein Condensation in Superconductivity

NASA Astrophysics Data System (ADS)

de Llano, Manuel

Unification of the BCS and the Bose-Einstein condensation (BEC) theories is surveyed in detail via a generalized BEC (GBEC) finite-temperature statistical formalism. Its major difference with BCS theory is that it can be diagonalized exactly. Under specified conditions it yields the precise BCS gap equation for all temperatures as well as the precise BCS zero-temperature condensation energy for all couplings, thereby suggesting that a BCS condensate is a BE condensate in a ternary mixture of kinematically independent unpaired electrons coexisting with equally proportioned weakly-bound two-electron and two-hole Cooper pairs. Without abandoning the electron-phonon mechanism in moderately weak coupling it suffices, in principle, to reproduce the unusually high values of Tc (in units of the Fermi temperature TF) of 0.01-0.05 empirically reported in the so-called "exotic" superconductors of the Uemura plot, including cuprates, in contrast to the low values of Tc/TF ≤ 10-3 roughly reproduced by BCS theory for conventional (mostly elemental) superconductors. Replacing the characteristic phonon-exchange Debye temperature by a characteristic magnon-exchange one more than twice in size can lead to a simple interaction model associated with spin-fluctuation-mediated pairing.

My Half-Hour with Einstein

NASA Astrophysics Data System (ADS)

Romer, Robert H.

2005-04-01

Midway during my first year as a Princeton graduate student (1952-53), I was given a letter of introduction to Einstein. Over a year later I finally worked up my courage to use it and -- as a result -- enjoyed a one-on-one conversation with him in the study of his home on Mercer Street. I will describe how my chance to meet Einstein arose and what I can remember of our memorable (to me if not to him) conversation. Among other things, we discussed the bomb, the new state of Israel, fossil horse brains, and evolution. (``Has there really been enough time for all those changes?'') We talked about the Einstein-Rosen-Podolsky problem - though not by that name, and I believe that it was the ``Bohm version'' that he asked me about. (``Do you really believe that if someone here measured the spin of an atom, it could affect the simultaneous measurement of the spin of another atom way over there?'') My major recollection is of my wish that I had been better prepared. As Ehrenfest once wrote: ``Nothing is shabbier than the feeling: now God has granted me the opportunity to meet this man, and I sat before him open-mouthed; how much I might have asked him -- but nothing at all occurred to me.''

VACUUM TRAP

DOEpatents

Gordon, H.S.

1959-09-15

An improved adsorption vacuum trap for use in vacuum systems was designed. The distinguishing feature is the placement of a plurality of torsionally deformed metallic fins within a vacuum jacket extending from the walls to the central axis so that substantially all gas molecules pass through the jacket will impinge upon the fin surfaces. T fins are heated by direct metallic conduction, thereby ol taining a uniform temperature at the adeorbing surfaces so that essentially all of the condensible impurities from the evacuating gas are removed from the vacuum system.

Hidden symmetries on toric Sasaki-Einstein spaces

NASA Astrophysics Data System (ADS)

Slesar, V.; Visinescu, M.; Vîlcu, G. E.

2015-05-01

We describe the construction of Killing-Yano tensors on toric Sasaki-Einstein manifolds. We use the fact that the metric cones of these spaces are Calabi-Yau manifolds. The description of the Calabi-Yau manifolds in terms of toric data, using the Delzant approach to toric geometries, allows us to find explicitly the complex coordinates and write down the Killing-Yano tensors. As a concrete example we present the complete set of special Killing forms on the five-dimensional homogeneous Sasaki-Einstein manifold T 1,1.

On the Einstein-Podolsky-Rosen Paradox

NASA Astrophysics Data System (ADS)

McWeeny, Roy

Central to the EPR paradox is a [`]thought experiment' in which two spins are initially coupled to a state with S = 0 and are then separated to a large distance, at which they can be separately observed. Quantum mechanics apparently predicts that the two spins remain forever coupled, but this conflicts with Einstein's principle of [`]locality' or [`]separability', according to which spatially well separated systems must be independent, no matter how strongly they have interacted in the past. It is now widely held that Einstein was wrong and that [`]non-locality' follows inevitably from quantum mechanics i.e. that even distant systems are never truly separable.

Forming a Bose-Einstein Condensate

NASA Image and Video Library

2014-09-26

This sequence of false-color images shows the formation of a Bose-Einstein condensate in the Cold Atom Laboratory prototype at NASA Jet Propulsion Laboratory as the temperature gets progressively closer to absolute zero.

Constraints on Bose-Einstein-condensed axion dark matter from the Hi nearby galaxy survey data

NASA Astrophysics Data System (ADS)

Li, Ming-Hua; Li, Zhi-Bing

2014-05-01

One of the leading candidates for dark matter is the axion or axionlike particle in the form of a Bose-Einstein condensate (BEC). In this paper, we present an analysis of 17 high-resolution galactic rotation curves from the Hi nearby galaxy survey (THINGS) data [F. Walter et al., Astron. J. 136, 2563 (2008)] in the context of the axionic Bose-Einstein condensed dark matter model. Assuming a repulsive two-body interaction, we solve the nonrelativistic Gross-Pitaevskii equation for N gravitationally trapped bosons in the Thomas-Fermi approximation. We obtain the maximum possible radius R and the mass profile M(r) of a dilute axionic Bose-Einstein condensed gas cloud. A standard least- χ2 method is employed to find the best-fit values of the total mass M of the axion BEC and its radius R. The local mass density of BEC axion dark matter is ρa ≃0.02 GeV /cm3, which agrees with that presented by Beck [C. Beck, Phys. Rev. Lett. 111, 231801 (2013)]. The axion mass ma we obtain depends not only on the best-fit value of R, but also on the s-wave scattering length a (ma∝a1/3). The transition temperature Ta of an axion BEC on galactic scales is also estimated. Comparing the calculated Ta with the ambient temperature of galaxies and galaxy clusters implies that a ˜10-3 fm. The corresponding axion mass is ma≃0.58 meV. We compare our results with others.

Education for Einstein's World.

ERIC Educational Resources Information Center

Barry, Marie Myles

Einstein, translated into a philosophy of education, views the factors governing man's qualities--his genes, his parents, his neighborhood, his church, his country, his world--as relative forces in his development, susceptible to infinite growth, and depending upon various combinations of experience. These experiences, in turn, depend upon nature…

Bianchi type-I universe in Lyra manifold with quadratic equation of state

NASA Astrophysics Data System (ADS)

Şen, R.; Aygün, S.

2017-02-01

In this study, we have solved Einstein field equations for Bianchi type I universe model in Lyra manifold with quadratic equation of state (EoS) p = ap(t)2 - ρ(t). Where α ≠0 is an important constant. Cosmic pressure, density and displacement vector (β2) are related with α constant. In this study β2 is a decreasing function of time and behaves like a cosmological constant. These solutions agree with the studies of Halford, Pradhan and Singh, Aygün et al., Agarwal et al., Yadav and Haque as well as SN Ia observations.

Towards thermodynamics of universal horizons in Einstein-æther theory.

PubMed

Berglund, Per; Bhattacharyya, Jishnu; Mattingly, David

2013-02-15

Holography grew out of black hole thermodynamics, which relies on the causal structure and general covariance of general relativity. In Einstein-æther theory, a generally covariant theory with a dynamical timelike unit vector, every solution breaks local Lorentz invariance, thereby grossly modifying the causal structure of gravity. However, there are still absolute causal boundaries, called "universal horizons," which are not Killing horizons yet obey a first law of black hole mechanics and must have an entropy if they do not violate a generalized second law. We couple a scalar field to the timelike vector and show via the tunneling approach that the universal horizon radiates as a blackbody at a fixed temperature, even if the scalar field equations also violate local Lorentz invariance. This suggests that the class of holographic theories may be much broader than currently assumed.

From the Classroom to Washington: Einsteins on Education Reform

ERIC Educational Resources Information Center

Hughes, Kent H., Ed.; Byers, Elizabeth A., Ed.

2010-01-01

The Woodrow Wilson International Center for Scholars was delighted to host a group of current and former Albert Einstein Distinguished Educator Fellows as they celebrated the 20th anniversary of the fellowship program. Outstanding math and science teachers in America's K-12 schools, the Einstein Fellows spend a year (or sometimes two) working on…

Theoretical analysis of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator

NASA Astrophysics Data System (ADS)

Shin, Y. M.; Ryskin, N. M.; Won, J. H.; Han, S. T.; Park, G. S.

2006-03-01

The basic theory of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator consisting of two two-cavity klystron amplifiers reversely coupled through input/output slots is theoretically investigated. Application of Kirchhoff's laws to the coupled equivalent RLC circuit model of the device provides four nonlinear coupled equations, which are the first-order time-delayed differential equations. Analytical solutions obtained through linearization of the equations provide oscillation frequencies and thresholds of four fundamental eigenstates, symmetric/antisymmetric 0/π modes. Time-dependent output signals are numerically analyzed with variation of the beam current, and a self-modulation mechanism and transition to chaos scenario are examined. The oscillator shows a much stronger multistability compared to a delayed feedback klystron oscillator owing to the competitions among more diverse eigenmodes. A fully developed chaos region also appears at a relatively lower beam current, ˜3.5Ist, compared to typical vacuum tube oscillators (10-100Ist), where Ist is a start-oscillation current.

Spatial Bose-Einstein Condensation.

ERIC Educational Resources Information Center

Masut, Remo; Mullin, William J.

1979-01-01

Analyzes three examples of spatial Bose-Einstein condensations in which the particles macroscopically occupy the lowest localized state of an inhomogeneous external potential. The three cases are (1) a box with a small square potential well inside, (2) a harmonic oscillator potential, and (3) randomly sized trapping potentials caused by…

Approaching Bose-Einstein Condensation

ERIC Educational Resources Information Center

Ferrari, Loris

2011-01-01

Bose-Einstein condensation (BEC) is discussed at the level of an advanced course of statistical thermodynamics, clarifying some formal and physical aspects that are usually not covered by the standard pedagogical literature. The non-conventional approach adopted starts by showing that the continuum limit, in certain cases, cancels out the crucial…

The Einstein tower : an intertexture of dynamic construction, relativity theory and astronomy

NASA Astrophysics Data System (ADS)

Hentschel, Klaus; Hentschel, Ann M.

This book focuses on the `Einstein Tower', an architecturally historic observatory built in Potsdam in 1920 to allow the German astronomer Erwin Finlay Freundlich to attempt to verify experimentally Einstein's general theory of relativity. Freundlich, who was the first German astronomer to show a genuine interest in Einstein's theory, managed to interest his architect friend Erich Mendelsohn in designing this unique building. To develop a full historical picture, the book interweaves several descriptive levels: the biography of Freundlich; the social context in which he interacted with teachers, co-workers, students, his patrons (including Einstein), and scientific opponents; the cognitive aspects of his attempts to verify Einstein's theory; the political milieu within the Berlin scientific research community; and a cross-national comparison of astrophysics. This is an interesting account of this unconventional tale in the history of science.

A Demonstration of Einstein's Equivalence of Gravity and Acceleration

ERIC Educational Resources Information Center

Newburgh, Ronald

2008-01-01

In 1907, Einstein described a "Gedankenexperiment" in which he showed that free fall in a gravitational field is indistinguishable from a body at rest in an elevator accelerated upwards in zero gravity. This paper describes an apparatus, which is simple to make and simple to operate, that acts as an observable footnote to Einstein's example. It…

Beyond Einstein: From the Big Bang to Black Holes

NASA Technical Reports Server (NTRS)

2005-01-01

How did the Universe begin? Does time have a beginning and an end? Does space have edges? The questions are clear and simple. They are as old as human curiosity. But the answers have always seemed beyond the reach of science. Until now. In their attempts to understand how space, time, and matter are connected, Einstein and his successors made three predictions. First, space is expanding from a Big Bang; second, space and time can tie themselves into contorted knots called black holes where time actually comes to a halt; third, space itself contains some kind of energy that is pull- ing the Universe apart. Each of these three predictions seemed so fantastic when it was made that everyone, including Einstein himself, regarded them as unlikely. Incredibly, all three have turned out to be true. Yet Einstein's legacy is one of deep mystery, because his theories are silent on three questions raised by his fantastic predictions: (1) What powered the Big Bang? (2) What happens to space, time, and matter at the edge of a black hole? (3) What is the mysterious dark energy pulling the Universe apart? The answers to these questions-which lie at the crux of where our current theories fail us-will lead to a profound, new understanding of the nature of time and space. To find answers, however, we must venture beyond Einstein. The answers require new theories, such as the inflationary Universe and new insights in high-energy particle theory. Like Einstein s theories, these make fantastic predictions that seem hard to believe: unseen dimensions and entire universes beyond our own. We must find facts to confront and guide these new theories. Powerful new technologies now make this possible. And NASA and its partners are developing an armada of space-based observatories to chart the path to discovery. Here is where the Beyond Einstein story begins. By exploring the three questions that are Einstein s legacy, we begin the next revolution in understanding our Universe. We plot our way

Astronomical and Cosmological Symbolism in Art Dedicated to Newton and Einstein

NASA Astrophysics Data System (ADS)

Sinclair, R.

2013-04-01

Separated by two and a half centuries, Isaac Newton (1642-1727) and Albert Einstein (1879-1955) had profound impacts on our understanding of the universe. Newton established our understanding of universal gravitation, which was recast almost beyond recognition by Einstein. Both discovered basic patterns behind astronomical phenomena and became the best-known scientists of their respective periods. I will describe here how artists of the 18th and 20th centuries represented the achievements of Newton and Einstein. Representations of Newton express reverence, almost an apotheosis, portraying him as the creator of the universe. Einstein, in a different age, is represented often as a comic figure, and only rarely do we find art that hints at the profound view of the universe he developed.

Einstein/Roosevelt Letters: A Unit.

ERIC Educational Resources Information Center

Bodle, Walter S.

1985-01-01

The letters in this unit of study intended for secondary students are facsimile reproductions of the correspondence between Albert Einstein and President Roosevelt on the possibility of constructing an atomic bomb. Classroom activities are also suggested. (RM)

Einstein unmasked

NASA Astrophysics Data System (ADS)

Foster, Brian

2008-09-01

This is a remarkable and, at times, bewilderingly diverse volume. Consisting of 20 essays that represent the proceedings of a conference held in 2005 in Berlin, Germany, during the International Year of Physics, it offers insights into Einstein's influence on a swathe of human activity. In the introduction the distinguished editors make some remarkable claims for the book, calling it "an unique attempt" and saying that "there is no better introduction to...string theory", while the first essay states "Not since Newton's Principia..." Clearly this is a volume that aspires to high standards.

Weak stability of the plasma-vacuum interface problem

NASA Astrophysics Data System (ADS)

Catania, Davide; D'Abbicco, Marcello; Secchi, Paolo

2016-09-01

We consider the free boundary problem for the two-dimensional plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the Maxwell system for the electric and the magnetic fields. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. We study the linear stability of rectilinear plasma-vacuum interfaces by computing the Kreiss-Lopatinskiĭ determinant of an associated linearized boundary value problem. Apart from possible resonances, we obtain that the piecewise constant plasma-vacuum interfaces are always weakly linearly stable, independently of the size of tangential velocity, magnetic and electric fields on both sides of the characteristic discontinuity. We also prove that solutions to the linearized problem obey an energy estimate with a loss of regularity with respect to the source terms, both in the interior domain and on the boundary, due to the failure of the uniform Kreiss-Lopatinskiĭ condition, as the Kreiss-Lopatinskiĭ determinant associated with this linearized boundary value problem has roots on the boundary of the frequency space. In the proof of the a priori estimates, a crucial part is played by the construction of symmetrizers for a reduced differential system, which has poles at which the Kreiss-Lopatinskiĭ condition may fail simultaneously.

Stability under scalar perturbations and quasinormal modes of 4D Einstein-Born-Infeld dilaton spacetime: exact spectrum

NASA Astrophysics Data System (ADS)

Destounis, Kyriakos; Panotopoulos, Grigoris; Rincón, Ángel

2018-02-01

We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein-Born-Infeld dilaton spacetime in 1+3 dimensions. Solving the full radial equation in terms of hypergeometric functions, we provide an exact analytical expression for the spectrum. We find that the frequencies are purely imaginary, and we confirm our results by computing them numerically. Although the scalar field that perturbs the black hole is electrically neutral, an instability similar to that seen in charged scalar perturbations of the Reissner-Nordström black hole is observed.

GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations II: Dynamics and stochastic simulations

NASA Astrophysics Data System (ADS)

Antoine, Xavier; Duboscq, Romain

2015-08-01

GPELab is a free Matlab toolbox for modeling and numerically solving large classes of systems of Gross-Pitaevskii equations that arise in the physics of Bose-Einstein condensates. The aim of this second paper, which follows (Antoine and Duboscq, 2014), is to first present the various pseudospectral schemes available in GPELab for computing the deterministic and stochastic nonlinear dynamics of Gross-Pitaevskii equations (Antoine, et al., 2013). Next, the corresponding GPELab functions are explained in detail. Finally, some numerical examples are provided to show how the code works for the complex dynamics of BEC problems.

Republication of: Geometrodynamics in the null case. Exact solutions of the field equations of the general theory of relativity III

NASA Astrophysics Data System (ADS)

Jordan, Pascual; Kundt, Wolfgang

2014-03-01

This is an English translation of a paper by Pascual Jordan and Wolfgang Kundt, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 3 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein's equations found until then. (Parts 1, 2 and 4 of the series have already been reprinted, part 5 will be printed as a Golden Oldie in near future.) This third paper shows how solutions of the Einstein-Maxwell equations with null Maxwell field can be incorporated into the scheme of geometrodynamics. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Charles Misner.

Pure field theories and MACSYMA algorithms

NASA Technical Reports Server (NTRS)

Ament, W. S.

1977-01-01

A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.

Comparison of vacuum and non-vacuum urine tubes for urinary sediment analysis.

PubMed

Topcuoglu, Canan; Sezer, Sevilay; Kosem, Arzu; Ercan, Mujgan; Turhan, Turan

2017-12-01

Urine collection systems with aspiration system for vacuum tubes are becoming increasingly common for urinalysis, especially for microscopic examination of the urine. In this study, we aimed to examine whether vacuum aspiration of the urine sample has any adverse effect on sediment analysis by comparing results from vacuum and non-vacuum urine tubes. The study included totally 213 urine samples obtained from inpatients and outpatients in our hospital. Urine samples were collected to containers with aspiration system for vacuum tubes. Each sample was aliquoted to both vacuum and non-vacuum urine tubes. Urinary sediment analysis was performed using manual microscope. Results were evaluated using chi-square test. Comparison of the sediment analysis results from vacuum and non-vacuum urine tubes showed that results were highly concordant for erythrocyte, leukocyte and epithelial cells (gamma values 1, 0.997, and 0.994, respectively; p < .001). Results were also concordant for urinary casts, crystals and yeast (kappa values 0.815, 0.945 and 1, respectively; p < .001). The results show that in urinary sediment analysis, vacuum aspiration has no adverse effect on the cellular components except on casts.

Implementing competency based admissions at the Albert Einstein College of Medicine.

PubMed

Kerrigan, Noreen; Akabas, Myles H; Betzler, Thomas F; Castaldi, Maria; Kelly, Mary S; Levy, Adam S; Reichgott, Michael J; Ruberman, Louise; Dolan, Siobhan M

2016-01-01

The Albert Einstein College of Medicine (Einstein) was founded in 1955 during an era of limited access to medical school for women, racial minorities, and many religious and ethnic groups. Located in the Bronx, NY, Einstein seeks to educate physicians in an environment of state-of-the-art scientific inquiry while simultaneously fulfilling a deep commitment to serve its community by providing the highest quality clinical care. A founding principle of Einstein, the basis upon which Professor Einstein agreed to allow the use of his name, was that admission to the student body would be based entirely on merit. To accomplish this, Einstein has long used a 'holistic' approach to the evaluation of its applicants, actively seeking a diverse student body. More recently, in order to improve its ability to identify students with the potential to be outstanding physicians, who will both advance medical knowledge and serve the pressing health needs of a diverse community, the Committee on Admissions reexamined and restructured the requirements for admission. These have now been categorized as four 'Admissions Competencies' that an applicant must demonstrate. They include: 1) cocurricular activities and relevant experiences; 2) communication skills; 3) personal and professional development; and 4) knowledge. The purpose of this article is to describe the process that resulted in the introduction and implementation of this competency based approach to the admission process.

Einstein: The Gourmet of Creativity.

ERIC Educational Resources Information Center

Greenberg, Joel

1979-01-01

Reports a psychiatrist's analysis of Einstein's personal account of how he developed the theory of relativity. The psychiatrist cites Janusian thinking, actively conceiving two or more opposite concepts simultaneously, as a characteristic of much creative thought in general. (MA)

Vacuum Bloch-Siegert shift in Landau polaritons with ultra-high cooperativity

NASA Astrophysics Data System (ADS)

Li, Xinwei; Bamba, Motoaki; Zhang, Qi; Fallahi, Saeed; Gardner, Geoff C.; Gao, Weilu; Lou, Minhan; Yoshioka, Katsumasa; Manfra, Michael J.; Kono, Junichiro

2018-06-01

A two-level system resonantly interacting with an a.c. magnetic or electric field constitutes the physical basis of diverse phenomena and technologies. However, Schrödinger's equation for this seemingly simple system can be solved exactly only under the rotating-wave approximation, which neglects the counter-rotating field component. When the a.c. field is sufficiently strong, this approximation fails, leading to a resonance-frequency shift known as the Bloch-Siegert shift. Here, we report the vacuum Bloch-Siegert shift, which is induced by the ultra-strong coupling of matter with the counter-rotating component of the vacuum fluctuation field in a cavity. Specifically, an ultra-high-mobility two-dimensional electron gas inside a high-Q terahertz cavity in a quantizing magnetic field revealed ultra-narrow Landau polaritons, which exhibited a vacuum Bloch-Siegert shift up to 40 GHz. This shift, clearly distinguishable from the photon-field self-interaction effect, represents a unique manifestation of a strong-field phenomenon without a strong field.

A complete public archive for the Einstein IPC

NASA Technical Reports Server (NTRS)

Helfand, David J.

1995-01-01

This report documents progress made in the period 24 Sept. 1993 - 23 Sept. 1995 on the project described in our proposal 'A Complete Public Archive for the Einstein IPC' which was approved under the Astrophysics Data Program in 1992. We have completed most of the principal objectives of the original proposal; a NFE was recently approved so that costs for publications in press can be covered and we can complete the public record for the Einstein IPC database.

Einstein and Rastall theories of gravitation in comparison

NASA Astrophysics Data System (ADS)

Darabi, F.; Moradpour, H.; Licata, I.; Heydarzade, Y.; Corda, C.

2018-01-01

We profit by a recent paper of Visser claiming that Rastall gravity is equivalent to Einstein gravity to compare the two gravitational theories in a general way. Our conclusions are different from Visser's ones. We indeed argue that these two theories are not equivalent. In fact, Rastall theory of gravity is an "open" theory when compared to Einstein general theory of relativity. Thus, it is ready to accept the challenges of observational cosmology and quantum gravity.

Rotor dynamic simulation and system identification methods for application to vacuum whirl data

NASA Technical Reports Server (NTRS)

Berman, A.; Giansante, N.; Flannelly, W. G.

1980-01-01

Methods of using rotor vacuum whirl data to improve the ability to model helicopter rotors were developed. The work consisted of the formulation of the equations of motion of elastic blades on a hub using a Galerkin method; the development of a general computer program for simulation of these equations; the study and implementation of a procedure for determining physical parameters based on measured data; and the application of a method for computing the normal modes and natural frequencies based on test data.

The trace anomaly and dynamical vacuum energy in cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mottola, Emil

2010-04-30

The trace anomaly of conformal matter implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. These poles may be described by a local effective action with massless scalar fields, which couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects at macroscopic scales. In an effective field theory approach, the effective action of the anomaly is an infrared relevant term that should be added to the Einstein-Hilbert action of classical General Relativity to take account of macroscopic quantum effects. The additional scalar degrees of freedom contained in this effectivemore » action may be understood as responsible for both the Casimir effect in flat spacetime and large quantum backreaction effects at the horizon scale of cosmological spacetimes. These effects of the trace anomaly imply that the cosmological vacuum energy is dynamical, and its value depends on macroscopic boundary conditions at the cosmological horizon scale, rather than sensitivity to the extreme ultraviolet Planck scale.« less

Cosmological singularities and bounce in Cartan-Einstein theory

NASA Astrophysics Data System (ADS)

Lucat, Stefano; Prokopec, Tomislav

2017-10-01

We consider a generalized Einstein-Cartan theory, in which we add the unique covariant dimension four operators to general relativity that couples fermionic spin current to the torsion tensor (with an arbitrary strength). Since torsion is local and non-dynamical, when integrated out it yields an effective four-fermion interaction of the gravitational strength. We show how to renormalize the theory, in the one-loop perturbative expansion in generally curved space-times, obtaining the first order correction to the 2PI effective action in Schwinger-Keldysh (in-in) formalism. We then apply the renormalized theory to study the dynamics of a collapsing universe that begins in a thermal state and find that—instead of a big crunch singularity—the Universe with torsion undergoes a bounce. We solve the dynamical equations (a) classically (without particle production); (b) including the production of fermions in a fixed background in the Hartree-Fock approximation and (c) including the quantum backreaction of fermions onto the background space-time. In the first and last cases the Universe undergoes a bounce. The production of fermions due to the coupling to a contracting homogeneous background speeds up the bounce, implying that the quantum contributions from fermions is negative, presumably because fermion production contributes negatively to the energy-momentum tensor. When compared with former works on the subject, our treatment is fully microscopic (namely, we treat fermions by solving the corresponding Dirac equations) and quantum (in the sense that we include fermionic loop contributions).

Einstein-aether theory with a Maxwell field: General formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balakin, Alexander B., E-mail: Alexander.Balakin@kpfu.ru; Lemos, José P.S., E-mail: joselemos@ist.utl.pt

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shearmore » and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.« less

49 CFR 570.56 - Vacuum brake assist unit and vacuum brake system.

Code of Federal Regulations, 2010 CFR

2010-10-01

.... The following requirements apply to vehicles with vacuum brake assist units and vacuum brake systems. (a) Vacuum brake assist unit integrity. The vacuum brake assist unit shall demonstrate integrity as... maintained on the pedal. (1) Inspection procedure. Stop the engine and apply service brake several times to...

Demonstrations with a Vacuum: Old Demonstrations for New Vacuum Pumps.

ERIC Educational Resources Information Center

Greenslade, Thomas B., Jr.

1989-01-01

Explains mechanisms of 19th-century vacuum pumps. Describes demonstrations using the pump including guinea and feather tube, aurora tube, electric egg, Gassiots cascade, air mill, bell in vacuum, density and buoyancy of air, fountain in vacuum, mercury shower, palm and bladder glasses, Bacchus demonstration, pneumatic man-lifter, and Magdeburg…

Focus on quantum Einstein gravity Focus on quantum Einstein gravity

NASA Astrophysics Data System (ADS)

Ambjorn, Jan; Reuter, Martin; Saueressig, Frank

2012-09-01

The gravitational asymptotic safety program summarizes the attempts to construct a consistent and predictive quantum theory of gravity within Wilson's generalized framework of renormalization. Its key ingredient is a non-Gaussian fixed point of the renormalization group flow which controls the behavior of the theory at trans-Planckian energies and renders gravity safe from unphysical divergences. Provided that the fixed point comes with a finite number of ultraviolet-attractive (relevant) directions, this construction gives rise to a consistent quantum field theory which is as predictive as an ordinary, perturbatively renormalizable one. This opens up the exciting possibility of establishing quantum Einstein gravity as a fundamental theory of gravity, without introducing supersymmetry or extra dimensions, and solely based on quantization techniques that are known to work well for the other fundamental forces of nature. While the idea of gravity being asymptotically safe was proposed by Steven Weinberg more than 30 years ago [1], the technical tools for investigating this scenario only emerged during the last decade. Here a key role is played by the exact functional renormalization group equation for gravity, which allows the construction of non-perturbative approximate solutions for the RG-flow of the gravitational couplings. Most remarkably, all solutions constructed to date exhibit a suitable non-Gaussian fixed point, lending strong support to the asymptotic safety conjecture. Moreover, the functional renormalization group also provides indications that the central idea of a non-Gaussian fixed point providing a safe ultraviolet completion also carries over to more realistic scenarios where gravity is coupled to a suitable matter sector like the standard model. These theoretical successes also triggered a wealth of studies focusing on the consequences of asymptotic safety in a wide range of phenomenological applications covering the physics of black holes, early

Bell Inequality, Einstein-Podolsky-Rosen Steering, and Quantum Metrology with Spinor Bose-Einstein Condensates.

PubMed

Wasak, Tomasz; Chwedeńczuk, Jan

2018-04-06

We propose an experiment, where the Bell inequality is violated in a many-body system of massive particles. The source of correlated atoms is a spinor F=1 Bose-Einstein condensate residing in an optical lattice. We characterize the complete procedure-the local operations, the measurements, and the inequality-necessary to run the Bell test. We show how the degree of violation of the Bell inequality depends on the strengths of the two-body correlations and on the number of scattered pairs. We show that the system can be used to demonstrate the Einstein-Podolsky-Rosen paradox. Also, the scattered pairs are an excellent many-body resource for the quantum-enhanced metrology. Our results apply to any multimode system where the spin-changing collision drives the scattering into separate regions. The presented inquiry shows that such a system is versatile as it can be used for the tests of nonlocality, quantum metrology, and quantum information.

Bell Inequality, Einstein-Podolsky-Rosen Steering, and Quantum Metrology with Spinor Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Wasak, Tomasz; Chwedeńczuk, Jan

2018-04-01

We propose an experiment, where the Bell inequality is violated in a many-body system of massive particles. The source of correlated atoms is a spinor F =1 Bose-Einstein condensate residing in an optical lattice. We characterize the complete procedure—the local operations, the measurements, and the inequality—necessary to run the Bell test. We show how the degree of violation of the Bell inequality depends on the strengths of the two-body correlations and on the number of scattered pairs. We show that the system can be used to demonstrate the Einstein-Podolsky-Rosen paradox. Also, the scattered pairs are an excellent many-body resource for the quantum-enhanced metrology. Our results apply to any multimode system where the spin-changing collision drives the scattering into separate regions. The presented inquiry shows that such a system is versatile as it can be used for the tests of nonlocality, quantum metrology, and quantum information.

Dynamical preparation of Einstein-Podolsky-Rosen entanglement in two-well Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Opanchuk, B.; He, Q. Y.; Reid, M. D.; Drummond, P. D.

2012-08-01

We propose to generate Einstein-Podolsky-Rosen (EPR) entanglement between groups of atoms in a two-well Bose-Einstein condensate using a dynamical process similar to that employed in quantum optics. A local nonlinear S-wave scattering interaction has the effect of creating spin squeezing at each well, while a tunneling coupling, analogous to a beam splitter in optics, introduces an interference between these fields that causes interwell entanglement. We consider two internal modes at each well so that the entanglement can be detected by measuring a reduction in the variances of the sums of local Schwinger spin observables. As is typical of continuous variable (CV) entanglement, the entanglement is predicted to increase with atom number. It becomes sufficiently strong at higher numbers of atoms so that the EPR paradox and steering nonlocality can be realized. The entanglement is predicted using an analytical approach and, for larger atom numbers, using stochastic simulations based on a truncated Wigner function approximation. We find generally that strong tunneling is favorable, and that entanglement persists and is even enhanced in the presence of realistic nonlinear losses.

Analysis of the moisture evaporation process during vacuum freeze-drying of koumiss and shubat

NASA Astrophysics Data System (ADS)

Shingisov, Azret Utebaevich; Alibekov, Ravshanbek Sultanbekovich

2017-05-01

The equation for the calculating of a moisture evaporation rate in the vacuum freeze-drying, wherein as a driving force instead of the generally accepted in the drying theory of Δt temperature difference, Δp pressure difference, Δc concentration difference, a difference of water activity in the product and the relative air humidity (a_{{w}} - \\varphi) is suggested. By using the proposed equation, the processes of vacuum freeze-drying of koumiss and shubat were analyzed, and it was found two drying periods: constant and falling. On the first drying period, a moisture evaporation rate of koumiss is j = 2.75 × 10-3 kg/(m2 h) and of shubat is j = 2.37 × 10-3 kg/(m2 h). On the second period, values decrease for koumiss from j = 2.65 × 10-3 kg/(m2 h) to j = 1.60 × 10-3 kg/(m2 h), and for shubat from j = 2.25 × 10-3 kg/(m2 h) to j = 1.62 × 10-3 kg/(m2 h). Specific humidity for koumiss is ueq = 0.61 kg/kg and for shubat is ueq = 0.58 kg/kg. The comparative analyze of the experimental data of the moisture evaporation rate versus the theoretical calculation shows that the approximation reliability is R2 = 0.99. Consequently, the proposed equation is useful for the analyzing a moisture evaporation rate during a vacuum freeze-drying of dairy products, including cultured milk foods.

Multi-vortex crystal lattices in Bose-Einstein condensates with a rotating trap.

PubMed

Xie, Shuangquan; Kevrekidis, Panayotis G; Kolokolnikov, Theodore

2018-05-01

We consider vortex dynamics in the context of Bose-Einstein condensates (BECs) with a rotating trap, with or without anisotropy. Starting with the Gross-Pitaevskii (GP) partial differential equation (PDE), we derive a novel reduced system of ordinary differential equations (ODEs) that describes stable configurations of multiple co-rotating vortices (vortex crystals). This description is found to be quite accurate quantitatively especially in the case of multiple vortices. In the limit of many vortices, BECs are known to form vortex crystal structures, whereby vortices tend to arrange themselves in a hexagonal-like spatial configuration. Using our asymptotic reduction, we derive the effective vortex crystal density and its radius. We also obtain an asymptotic estimate for the maximum number of vortices as a function of rotation rate. We extend considerations to the anisotropic trap case, confirming that a pair of vortices lying on the long (short) axis is linearly stable (unstable), corroborating the ODE reduction results with full PDE simulations. We then further investigate the many-vortex limit in the case of strong anisotropic potential. In this limit, the vortices tend to align themselves along the long axis, and we compute the effective one-dimensional vortex density, as well as the maximum admissible number of vortices. Detailed numerical simulations of the GP equation are used to confirm our analytical predictions.

Improved Vacuum Bazooka

NASA Astrophysics Data System (ADS)

Cockman, John

2003-04-01

This apparatus is a modification to the well-known "vacuum bazooka" (PIRA 2B30.70). My vacuum bazooka is easy to construct and demonstrate, requires no precise fittings, foil, or vacuum grease, and propels ping-pong balls at a tremendous velocity!

Einstein, Picasso

NASA Astrophysics Data System (ADS)

Miller, Arthur I.

2004-11-01

How the 20th century’s most important scientist—Albert Einstein—and its most important artist—Pablo Picasso—made their greatest discoveries at almost the same time is a remarkable story: Einstein's relativity theory in 1905 and Picasso's Les Demoiselles d'Avignon two years later. A scientist and an artist confronted the same problem—the nature of time and simultaneity—and resolved it after realizing a new aesthetic. At the nascent moment of creativity boundaries dissolve between disciplines. This article explores the similarities in the early work of two of the greatest icons of Art and Science of the last century.

Nonperturbative Dynamical Casimir Effect in Optomechanical Systems: Vacuum Casimir-Rabi Splittings

NASA Astrophysics Data System (ADS)