Static Gravitational Field Research Articles

Vector-field domain walls

We argue that spontaneous Lorentz violation may generally lead to metastable domain walls related to the simultaneous violation of some accompanying discrete symmetries. Remarkably, such domain-wall solutions exist for spacelike Lorentz violation and do not exist for the timelike violation. Because a preferred space direction is spontaneously induced, these domain walls have no planar symmetry and produce a peculiar static gravitational field at small distances, while their long-distance gravity appears the same as for regular scalar-field walls. Some possible applications of vector-field domain walls are briefly discussed.

Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations

An exact solution of Einstein’s equations representing the static gravitational field of a quasi-spherical source endowed with both mass and mass quadrupole moment is considered. It belongs to the Weyl class of solutions and reduces to the Schwarzschild solution when the quadrupole moment vanishes. The geometric properties of timelike circular orbits (including geodesics) in this spacetime are investigated. Moreover, a comparison between geodesic motion in the spacetime of a quasi-spherical source and non-geodesic motion of an extended body also endowed with both mass and mass quadrupole moment as described by Dixon’s model in the gravitational field of a Schwarzschild black hole is discussed. Certain “reciprocity relations” between the source and the particle parameters are obtained, providing a further argument in favor of the acceptability of Dixon’s model for extended bodies in general relativity.

Hard thermal loops in static external fields

We examine, in the imaginary-time formalism, the high temperature behavior of $n$-point thermal loops in static Yang-Mills and gravitational fields. We show that in this regime, any hard thermal loop gives the same leading contribution as the one obtained by evaluating the loop integral at zero external energies and momenta.

On Relativistic Generalization of Gravitational Force

In relativistic theories, the assumption of proper mass constancy generally holds. We study gravitational relativistic mechanics of point particle in the novel approach of proper mass varying under Minkowski force action. The motivation and objective of this work are twofold: first, to show how the gravitational force can be included in the Special Relativity Mechanics framework, and, second, to investigate possible consequences of the revision of conventional proper mass concept (in particular, to clarify a proper mass role in the divergence problem). It is shown that photon motion in the gravitational field can be treated in terms of massless refracting medium, what makes the gravity phenomenon compatible with SR Mechanics framework in the variable proper mass approach. Specifically, the problem of point particle in the spherical symmetric stationary gravitational field is studied in SR-based Mechanics, and equations of motion in the Lorentz covariant form are obtained in the relativistic Lagrangean problem formulation. The dependence of proper mass on potential field strength is derived from the Euler-Lagrange equations as well. One of new results is the elimination of conventional 1/r divergence, which is known to be not removable in Schwarzschild gravitomechanics. Predictions of particle and photon gravitational properties are in agreement with GR classical tests under weak-field conditions; however, deviations rise with potential field strength. The conclusion is made that the approach of field-dependent proper mass is perspective for development of SR gravitational mechanics and further studies of gravitational problems.

Transition rate of the Unruh–DeWitt detector in curved spacetime

We examine the Unruh–DeWitt particle detector coupled to a scalar field in an arbitrary Hadamard state in four-dimensional curved spacetime. Using smooth switching functions to turn on and off the interaction, we obtain a regulator-free integral formula for the total excitation probability, and we show that an instantaneous transition rate can be recovered in a suitable limit. Previous results in Minkowski space are recovered as a special case. As applications, we consider an inertial detector in the Rindler vacuum and a detector at rest in a static Newtonian gravitational field. Gravitational corrections to decay rates in atomic physics laboratory experiments on the surface of the Earth are estimated to be suppressed by 42 orders of magnitude.

General relativity constrains proper times and predicts frozen stars instead of black holes

In a static gravitational field an intersection of a worldline by a global hypersurface of simultaneity t=const gives an invariant constraint relating the proper time of this event by t. Since at any finite t the such constrained proper time intervals are less than reqiured for crossing a horizon, general relativity predicts the gravitational freezing of proper times in stars with time-like or null geodesics everywhere. The time dilation stabilizes contracting massive stars by freezing, which is maximal but finite at the centre, and the surface is frozen near the gravitational radius. The frozen stars (frozars) slowly defrost due to emissions and external interactions, the internal phase transitions can initiate refreezing with bursts and explosions.

Energy-level shifts of a stationary hydrogen atom in a static external gravitational field with Schwarzschild geometry

The first order perturbations of the energy levels of a stationary hydrogen atom in a static external gravitational field, with Schwarzschild metric, are investigated. The energy shifts are calculated for the relativistic $1S$, $2S$, $2P$, $3S$, $3P$, $3D$, $4S$, $4P$, $4D$, and $4F$ levels. The results show that the energy-level shifts of the states with total angular momentum quantum number $1/2$ are all zero, and the ratio of absolute energy shifts with total angular momentum quantum number $5/2$ is $1\ensuremath{\mathbin:}4\ensuremath{\mathbin:}5$. This feature can be used to help us to distinguish the gravitational effect from other effects.

Double Superpotential and Generation of New Solutions of Stationary Axisymmetric Gravitational Fields

In this paper COX’s superpotential is extended to double complex form firstly, then how to get hyperbolic complex superpotential from the known ordinary complex superpotential is discussed, finally, new solutions of stationary axisymmetric gravitational fields are shown with a few specific cases.

Stationary perfect fluid solutions with differential rotation

In the framework of a class of metrics allowing for a timelike and a spacelike symmetries, usually referred to as stationary and axisymmetric gravitational fields, coupled to differentially rotating perfect fluids, the existing exact solutions to the corresponding Einstein equations are analyzed from the point of view of the fulfillment of the energy conditions and the existence of an axis of rotation. The main conclusion is that none of the reported exact solutions fulfills all these physical requirements, and at most, they can be thought of as stationary cyclic symmetric cosmological spacetimes.

Semiclassical diagonalization of quantum Hamiltonian and equations of motion with Berry phase corrections

It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum systems may be affected by Berry phase terms. It is therefore important to find a general procedure allowing for the determination of semiclassical Hamiltonian with Berry Phase corrections. This article presents a general diagonalization method at order $\hbar $ for a large class of quantum Hamiltonians directly inducing Berry phase corrections. As a consequence, Berry phase terms on both coordinates and momentum operators naturally arise during the diagonalization procedure. This leads to new equations of motion for a wide class of semiclassical system. As physical applications we consider here a Dirac particle in an electromagnetic or static gravitational field, and the propagation of a Bloch electrons in an external electromagnetic field.

Phase transitions in dense quark matter in a gravitational field of constant curvature

The impact of the gravitational field on the formation of quark and diquark condensate in the framework of the extended Nambu-Jona-Lasinio (NJL) model is studied. In the mean field approximation, an expression for the effective potential with regard to a finite temperature and density of quark matter in the static gravitational field of constant curvature is obtained.

A simple optical analysis of gravitational lensing

We analysed the influence of a static gravitational field on the vacuum and discussed the concept of an inhomogeneous vacuum. According to the corresponding Fermat's principle in general relativity, we derived a graded refractive index of vacuum in a static gravitational field. We found that the light deflection in a gravitational field can be calculated correctly with the use of this refractive index and therefore the gravitational lensing can be treated conveniently with the optical method. For illustration, we simulated the imaging of gravitational lensing, figured out the time delay between the two images and calculated the lens mass in a conventional optical way.

Spin Hall effect of photons in a static gravitational field

Starting from a Hamiltonian description of the photon within the set of Bargmann-Wigner equations we derive new semiclassical equations of motion for the photon propagating in static gravitational field. These equations which are obtained in the representation diagonalizing the Hamiltonian at the order $\hbar $, present the first order corrections to the geometrical optics. The photon Hamiltonian shows a new kind of helicity-magnetotorsion coupling. However, even for a torsionless space-time, photons do not follow the usual null geodesic as a consequence of an anomalous velocity term. This term is responsible for the gravitational birefringence phenomenon: photons with distinct helicity follow different geodesics in a static gravitational field.

Semiclassical dynamics of Dirac particles interacting with a static gravitational field

The semiclassical limit for Dirac particles interacting with a static gravitational field is investigated. A Foldy-Wouthuysen transformation which diagonalizes at the semiclassical order the Dirac equation for an arbitrary static spacetime metric is realized. In this representation the Hamiltonian provides for a coupling between spin and gravity through the torsion of the gravitational field. In the specific case of a symmetric gravitational field we retrieve the Hamiltonian previously found by other authors. But our formalism provides for another effect, namely, the spin hall effect, which was not predicted before in this context.

Publisher’s Note: Energy and angular momentum densities of stationary gravitational fields [Phys. Rev. D75, 024040 (2007)

Publisher’s Note: Energy and angular momentum densities of stationary gravitational fields [Phys. Rev. D<b>75</b>, 024040 (2007)

Energy and angular momentum densities of stationary gravitational fields

We give physical explanations of explicit invariant expressions for the energy and angular momentum densities of gravitational fields in stationary spacetimes. These expressions involve nonlocally defined conformal factors. In certain coordinates these become locally defined in terms of the metric. These results are derived via expressions for total gravitational potential energy from the difference between the total energy and the mechanical energy. The latter involves kinetic energy seen in the frame of static observers. When in the axially symmetric case we consider zero angular momentum observers (who move orthogonally to surfaces of constant time), we find that the angular momentum they attribute to the gravitational field is solely due to their motion.

Vibration effect on morphological instability of planar solidification front

This paper deals with the effects of vibrations on the stability of a binary alloy solidifying at constant velocity under zero gravity conditions or in the presence of a static gravitational field. The density dependence of the solute concentration is accounted for through the Boussinesq approximation. In the first part of the paper, the effect of finite frequency vibrations normal to the planar interface is studied numerically. It is found that at large frequencies vibrations have a destabilizing effect. For lower frequencies, a parameter range is found where vibrations exert a strong stabilizing effect. In the second part of the paper, the influence of high-frequency vibrations is studied. Equations for the average velocity and concentration fields are obtained by a multiple scale method. It is found that vibrations normal to the interface exert a destabilizing effect, whereas tangential vibrations may suppress the onset of morphological stability.

Forgetting and gravitation: From Landauer's principle to Tolman's temperature

The erasure of a bit of information requires the dissipation of a minimal amount of energy as being formulated in Landauer's principle. We show that for an information processing device in a static gravitational field Landauer's lower energy bound is determined by Tolman's temperature relation.

Active mass under pressure

After a historical introduction to Poisson’s equation in Newtonian gravity, we review its analog for static gravitational fields in Einstein’s theory. The source of the potential, which we call the active mass density, comprises not only all possible sources of energy, but also the pressure term 3P∕c2. In the Hamburg seminar on relativity in the 1950s we discussed whether this term due to Fermi pressure in different atomic nuclei could be detected in Cavendish-type experiments. Our reasoning contained an instructive mistake that we are now able to resolve. We conclude that this term should not lead to discrepancies for different materials in a Cavendish-type experiment, although it is important in the early universe and collapsing stellar cores.

The Clock Paradox in a Static Homogeneous Gravitational Field1

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars.