Influence of Dark Energy on Gravitational Time Delay

We investigate the gravitational time delay of light in the Schwarzschild black hole space-time surrounded by quintessence. With the analysis and numerical methods, we find that the gravitational time delay of light in the Schwarzschild black hole space-time surrounded by quintessence increases when the normalization factor c increases, and that the gravitational time delay also decreases when the quintessential state parameter ω_q increases.     

Interference Phase of Mass Neutrinos in Kerr Space-Time

Along the geodesic we calculate the interference phase of the mass neutrinos in some special cases. Because of the rotation of the mass resource which induces the gravitational field, the angular momentum per unit mass, a, has a contribution to the phase, which is different from the case in Schwarzschild space-time.     

Interference Phase of Mass Neutrinos in Kerr Space-Time

Along the geodesic we calculate the interference phase of the mass neutrinos in some special cases. Because of the rotation of the mass resource which induces the gravitational field, the angular momentum per unit mass, a, has a contribution to the phase, which is different from the case in Schwarzschild space-time.     

Gravitational Corrections to Energy-Levels of a Hydrogen Atom

The first-order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number.     

Quantum long-range interactions in general relativity

We consider one-loop effects in general relativity that result in quantum long-range corrections to the Newton law, as well as to the gravitational spin-dependent and velocity-dependent interactions. Some contributions to these effects can be interpreted as quantum corrections to the Schwarzschild and Kerr metrics.     

Gravitational frequency-shift and deflection of light by quintessence

In this paper we investigate the gravitational frequency-shift and deflection of light in the Schwarzschild black hole space-time surrounded by quintessence. With the analytical and numerical methods, we find that the gravitational frequency-shift of light in the Schwarzschild black hole space-time surrounded by the quintessence increases as the values of the normalization factor $c$ increases, but the gravitational frequency-shift of light decreases with the quintessential state parameter $ \omega_{\rm q}$ increasing. We also calculate the deflection of light by quintessence and find that the deflection rate decreases as the values of the quintessential parameters $c$ and $ \omega_{\rm q}$ increase.     

Metric gravitation with a two parameter family of static spherically symmetric space-times

Among the variety of all conceivable metric theories of gravitation, Lorentz curvature dynamics is the most geometric extension of Einstein's field equations to fit the solar system data. In this framework two parameters determine the asymptotic form of a static spherically symmetric space-time (without imposing Einstein's conditions); these two parameters are the active gravitational mass of the source and the PPN parameter γ. The Lorentz connection is shown to satisfy covariant evolution equations which preserve either of these two parameters; furthermore, right and left oriented space-times differ in their Lorentz connection. Deviations from the Schwarzschild character find an interpretation in terms of a new object, the Lorentz curvature energy-momentum tensor, which always vanishes identically under the restriction of Einstein's conditions. These deviations contribute strongly to the gravitational force only in the neighbourhood of the Schwarzschild sphere.     

Gravitational effects on the neutrino oscillation in vacuum

The propagation of neutrinos in a gravitational field is studied by developing a method of calculating a covariant quantum-mechanical phase in a curved space-time. The result is applied to neutrino propagation in the Schwarzschild metric.     

Ultimate gravitational mass defect

We present a new type of gravitational mass defect in which an infinite amount of matter may be bounded in a zero ADM mass. This interpolates between effects typical of closed worlds and T-spheres. We consider the Tolman model of dust distribution and show that this phenomenon reveals itself for a solution that has no origin on one side but is closed on the other side. The second class of examples corresponds to smooth gluing T-spheres to the portion of the Friedmann-Robertson-Walker solution. The procedure is generalized to combinations of smoothly connected T-spheres, FRW and Schwarzschild metrics. In particular, in this approach a finite T-sphere is obtained that looks for observers in two R-regions as the Schwarzschild metric with two different masses one of which may vanish.     

SPHERICALLY SYMMETRIC AND STATIC FIELDS IN LINEARIZED GAUGE THEORIES OF GRAVITATION

In this paper Newtonian limit in the Poincare gauge field theory of gravitation is investigated. In spherically symmetric and static cases interior and exterior solutions of the linearized field equations with gravitational sourtion are obtained by maens of Green's function for the five Lagrangians with out ghosts and tachyons. In cases of four Lagrangians,the space-time metrics outside gravitational source are the usual Schwarzschild one of the first-older, while in the case of the fifth hagrangian the space-time metric differs from the Schwarzschild one. Under both,Newtonian and-weak gravitational field approximations,the motion of a test particle without span should therefore be different from Newton's second law. As a result of the exchanged particles of spin o⁺ the deviation from Newton's second law is a Yukawa term which is attractive. A distance-dependent gravitational "constant" G(r) can be defined according to the new result. The difference between G(r) and Newton's gravitational constant G_∞ is due to a nonzero component of torsion tensor, the effect of which can be tested by measuring G(r).     

A source of a quasi-spherical space–time: The case for the <Emphasis Type="Italic">M</Emphasis>–<Emphasis Type="Italic">Q</Emphasis> solution

We present a physically reasonable source for an static, axially-symmetric solution to the Einstein equations. Arguments are provided, supporting our belief that the exterior space-time produced by such source, describing a quadrupole correction to the Schwarzschild metric, is particularly suitable (among known solutions of the Weyl family) for discussing the properties of quasi-spherical gravitational fields.     

Geodesies in the Erez-Rosen space-time

We investigate null and time-like geodesics in the Erez-Rosen space-time, that is, in the exterior gravitational field of a mass with quadrupole moment. By using the weak-field approximation of the Erez-Rosen metric, we find the solution of the equation for equatorial time-like geodesics and determine how they differ from the corresponding Schwarzschild geodesies. For the exact form of the Erez-Rosen metric, we only draw some qualitative conclusions about the influence of the quadrupole moment on the path of test particles and on the motion of photons. We derive the relativistic contribution of the quadrupole moment to the perihelion shift and to the precession of the ascending node.     

Spherical symmetry and mass-energy in higher dimensions

The components of the Einstein tensor and other relations are given for a spherically symmetric metric in null coordinates in higher dimensions. These relations are particularly relevant to the study of gravitational collapse of a perfect fluid with heat flow but without viscosity, where the exterior space cannot be considered as vacuum and matching to Schwarzschild space-time is not suitable. The analysis generalizes to higher dimensions work of Cahill and McVittie in 4D space-time. Using the expression for the mass function, it is observed that pressure vanishes at the boundary of the distribution for a perfect fluid in the higher-dimensional case also, but the same is not true when heat flow is considered.     

Tachyons in general relativity

The tachyonic version of the Schwarzschild (bradyonic) gravitational field within the framework of extended relativity is considered. The metric of a tachyonic black hole is obtained through superluminal transformations from a bradyonic metric. The extended space-time manifold of this geometry which includes both black and white tachyonic holes is analysed, and the differences between the tachyonic and bradyonic versions are noted. It is shown that the meanings of black holes, tachyons and bradyons depend on the character of the reference frame and are not absolute.     

Quantum fluctuations in the conformally flat and the schwarzschild space-times

A general technique is described for dealing with the quantum fluctuations between conformally flat space-times. The second part of the paper deals with the Schwarzschild spacetime. It is shown there that this space-time is stable against fluctuations of mass, but transitions between two space-times of different masses can be obtained via conformai fluctuations. Purely conformal fluctuations of the Schwarzschild metric are, however, damped at the event horizon. Similar conclusions are drawn about the Reissner-Nordstrom space-time.     

The Sagnac effect in curved space-times from an analogy with the Aharonov-Bohm effect

In the context of the natural splitting, the standard relative dynamics can be expressed in terms of gravito-electromagnetic fields, which allow to formally introduce a gravito-magnetic Aharonov-Bohm effect. We showed elsewhere that this formal analogy can be used to derive the Sagnac effect in flat space-time as a gravito-magnetic Aharonov-Bohm effect. Here, we generalize those results to study the General Relativistic corrections to the Sagnac effect in some stationary and axially symmetric geometries, such as the space-time around a weakly gravitating and rotating source, Kerr space-time, Gödel universe and Schwarzschild space-time.     

The homogeneous gravitational field

The homogeneous gravitational field is obtained from a Schwarzschild field in the limit of infinite mass.Dedicated to Peter Bergmann on his 70th birthday.     

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.     

Exact Harmonic Metric for a Uniformly Moving Schwarzschild Black Hole

The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.