Sagnac Effect in the Kerr-Newman and Reissner-Nordstrom Fields

By means of a formal analogy with the Aharonov-Bohm effect, the Sagnac time delay and the corresponding Sagnac phase shift in the Kerr-Newman and Reissner-Nordstrfm spacetimes are discussed. We find that the effect depends on the properties of the source of the gravitational field. The contributions made by the electric charge of the gravitational source can be employed to weaken it in the Kerr-Newman spacetime, even if a phase shift and a time delay still appear. This is due to the properties of the rotating source of the gravitational field.     

Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime

The strong similarities between the light propagation in a curved spacetime and that in a medium with graded refractive index are found. It is pointed out that a curved spacetime is equivalent to an inhomogeneous vacuum for light propagation. The corresponding graded refractive index of the vacuum in a static spherically symmetrical gravitational field is derived. This result provides a simple and convenient way to analyse the gravitational lensing in astrophysics.     

Stochastic Spacetime and Brownian Motion of Test Particles

The operational meaning of spacetime fluctuations is discussed. Classical spacetime geometry can be viewed as encoding the relations between the motions of test particles in the geometry. By analogy, quantum fluctuations of spacetime geometry can be interpreted in terms of the fluctuations of these motions. Thus, one can give meaning to spacetime fluctuations in terms of observables which describe the Brownian motion of test particles. We will first discuss some electromagnetic analogies, where quantum fluctuations of the electromagnetic field induce Brownian motion of test particles. We next discuss several explicit examples of Brownian motion caused by a fluctuating gravitational field. These examples include lightcone fluctuations, variations in the flight times of photons through the fluctuating geometry, and fluctuations in the expansion parameter given by a Langevin version of the Raychaudhuri equation. The fluctuations in this parameter lead to variations in the luminosity of sources. Other phenomena that can be linked to spacetime fluctuations are spectral line broadening and angular blurring of distant sources.     

Relativistic motion of a free particle in a uniform gravitational field

The problem of the motion of a free particle in a uniform gravitational field is considered. A relativistic solution based on the assumption that the motion is a consequence of the curvature of spacetime is obtained. The results are compared with various results based on the assumption that spacetime is flat in a region in which the gravitational field is uniform. In the curved spacetime approach, if a particle is projected from a point in a uniform gravitational field, the vertical distance covered by the particle in infinite coordinate time is infinite, but the horizontal distance covered and the elapsed proper time of the particle are finite. If spacetime is assumed to be flat and the gravitational motion of a particle a consequence of a relativistic force proportional to the relative mass of the particle, then the results obtained for the motion of a particle in a uniform gravitational field are close to the curved spacetime results. All other assumptions, including the assumption that the motion of a particle in a uniform gravitational field is equivalent to the motion of a particle in a uniformly accelerating frame of reference, lead to results in serious disagreement with the curved spacetime results.     

Conformally Flat Spacetimes and Weyl Frames

We discuss the concepts of Weyl and Riemann frames in the context of metric theories of gravity and state the fact that they are completely equivalent as far as geodesic motion is concerned. We apply this result to conformally flat spacetimes and show that a new picture arises when a Riemannian spacetime is taken by means of geometrical gauge transformations into a Minkowskian flat spacetime. We find out that in the Weyl frame gravity is described by a scalar field. We give some examples of how conformally flat spacetime configurations look when viewed from the standpoint of a Weyl frame. We show that in the non-relativistic and weak field regime the Weyl scalar field may be identified with the Newtonian gravitational potential. We suggest an equation for the scalar field by varying the Einstein-Hilbert action restricted to the class of conformally-flat spacetimes. We revisit Einstein and Fokker’s interpretation of Nordstr?m scalar gravity theory and draw an analogy between this approach and the Weyl gauge formalism. We briefly take a look at two-dimensional gravity as viewed in the Weyl frame and address the question of quantizing a conformally flat spacetime by going to the Weyl frame.     

Global Properties of Gravitational Lens Maps¶in a Lorentzian Manifold Setting

In a general-relativistic spacetime (Lorentzian manifold), gravitational lensing can be characterized by a lens map, in analogy to the lens map of the quasi-Newtonian approximation formalism. The lens map is defined on the celestial sphere of the observer (or on part of it) and it takes values in a two-dimensional manifold representing a two-parameter family of worldlines. In this article we use methods from differential topology to characterize global properties of the lens map. Among other things, we use the mapping degree (also known as Brouwer degree) of the lens map as a tool for characterizing the number of images in gravitational lensing situations. Finally, we illustrate the general results with gravitational lensing (a) by a static string, (b) by a spherically symmetric body, (c) in asymptotically simple and empty spacetimes, and (d) in weakly perturbed Robertson–Walker spacetimes. Received: 16 October 2000 / Accepted: 18 January 2001     

Gravitational Wave in Lorentz Violating Gravity

By making use of the weak gravitational field approximation, we obtain a linearized solution of the gravitational vacuum field equation in an anisotropic spacetime. The plane-wave solution and dispersion relation of gravitationaJ wave is presented explicitly. There is possibility that the speed of gravitational wave is larger than the speed of light and the easuality still holds. We show that the energy-momentum of gravitational wave in the ansiotropic spacetime is still well defined and conserved.     

Gravitational Wave in Lorentz Violating Gravity

By making use of the weak gravitational field approximation, we obtain a linearized solution of the gravitational vacuum field equation in an anisotropic spacetime. The plane-wave solution and dispersion relation of gravitational wave is presented explicitly. There is possibility that the speed of gravitational wave is larger than the speed of light and the casuality still holds. We show that the energy-momentum of gravitational wave in the ansiotropic spacetime is still well defined and conserved.     

Gravitational energy-momentum density in teleparallel gravity

In the context of a gauge theory for the translation group, a conserved energy-momentum gauge current for the gravitational field is obtained. It is a true spacetime and gauge tensor, and transforms covariantly under global Lorentz transformations. By rewriting the gauge gravitational field equation in a purely spacetime form, it becomes the teleparallel equivalent of Einstein's equation, and the gauge current reduces to the Moller's canonical energy-momentum density of the gravitational field.     

Massive scalar counterpart of gravitational waves in scalarized neutron star binaries

In analogy with spontaneous magnetization of ferromagnets below the Curie temperature, a neutron star (NS), with a compactness above a certain critical value, may undergo spontaneous scalarization and exhibit an interior nontrivial scalar configuration. Consequently, the exterior spacetime is changed, and an external scalar field appears, which subsequently triggers a scalarization of its companion. The dynamical interplay produces a gravitational scalar counterpart of tensor gravitational waves. In this paper, we resort to scalar–tensor theory and demonstrate that the gravitational scalar counterpart from a double neutron star (DNS) and a neutron star–white dwarf (NS-WD) system become massive. We report that (1) a gravitational scalar background field, arising from convergence of external scalar fields, plays the role of gravitational scalar counterpart in scalarized DNS binary, and the appearance of a mass-dimensional constant in a Higgs-like gravitational scalar potential is responsible for a massive gravitational scalar counterpart with a mass of the order of the Planck scale; (2) a dipolar gravitational scalar radiated field, resulting from differing binding energies of NS and WD, plays the role of a gravitational scalar counterpart in scalarized orbital shrinking NS-WDs, which oscillates around a local and scalar-energy-density-dependent minimum of the gravitational scalar potential and obtains a mass of the order of about \(10^{-21}\,{\text {eV/c}}^2\).     

The Gravitational Energy–Momentum Density of Radially Accelerated Observers in Schwarzschild Spacetime

A hybrid machinery that is useful for calculations in teleparallel theories when the spacetime is spherically symmetric is developed. Using this machinery, the gravitational energy–momentum tensor density of the Schwarzschild spacetime is evaluated in a frame adapted to observers that accelerate in the radial direction. The energy density, the total energy, and the gravitational energy-momentum flux are obtained. The regularization procedure and the limit where gravity is absent is discussed. It turns out that the regularized energy and energy–momentum flux are consistent in the whole spacetime. The continuity equation for the gravitational energy–momentum also holds for any point outside the black hole. Finally, the static and freely falling cases are discussed. It is found that a static observer measures a negative gravitational energy density, while a freely falling one measures a vanishing density.     

The Clifford bundle and the nature of the gravitational field

In this paper we formulate Einstein's gravitational theory with the Clifford bundle formalism. The formalism suggests interpreting the gravitational field in the sense of Faraday, i.e., with the field residing in Minkowski spacetime. We succeeded in discovering the condition for this interpretation to hold. For the variables that play the role of the gravitational field in our theory, the Lagrangian density turns out to be of the Yang-Mills type (with an auto-interaction plus gauge-fixing terms). We give a brief comparison of our theory with other field theories of the gravitational field in the flat Minkowski spacetime.     

Gauge and gravitational anomalies and Hawking radiation of rotating BTZ black holes

In this paper we obtain the flux of Hawking radiation from rotating BTZ black holes from the gauge and gravitational anomalies point of view. Then we show that the gauge and gravitational anomaly in BTZ spacetime is cancelled by the total flux of a 2-dimensional blackbody at the Hawking temperature of the spacetime.     

On Sakharov's theory of gravitation

The Sakharov theory of gravitation is examined from the viewpoint of the analogy between gravitation and elasticity. It is found that, by using the Cattaneo-Zel'manov projection technique, the deformation tensor connected with the gravitational field can be considered the deformation tensor of a suitable elastic medium. By supposing that transversal waves propagate in this medium with velocityc, one can find an explicit expression for the time dependence of the gravitational constant. Some applications of cosmological interest are briefly discussed.     

Spherically Symmetric Wormhole Gravitational Lens Deflection Angle Signifying Braneworld Cosmology

Previously, the gravitational lens of a wormhole was introduced by various researchers. Their treatment was focused basically on the lens signature that describes wormhole geometrical character such as the differences from a black hole or between any various types of wormhole models. The braneworld scenario provides the idea of spacetime with underlying extra-dimensions. The inclusion of extra-dimensional terms in the lens object spacetime line element will result in some variation in the expression for its gravitational lens deflection angle.Thus in this paper we investigate such variation by deriving this deflection angle expression. As such, this paper not only shows the existence of such variation but also suggests the potential utilization of gravitational lensing to prove the existence of extra dimensions by studying the deflection angle characteristic in accordance with the spacetime expansion rate of the universe.     

Does Charge Contribute to the Frame Dragging of?Spacetime?

Electrically charged systems bound by a strong gravitational force can sustain a huge amount of electric charge (up to 10²⁰ C) against Coulomb repulsion. General relativistically such systems form a stable hydrostatic configuration both in the non-rotating and rotating cases. Here we study the effects of electric charge (electric energy density) on the spacetime outside a rotating electrically charged system bound by a strong gravitational force. In particular we investigate the effect of charge density on frame-dragging of spacetime in the exterior region. Using the coupled Einstein-Maxwell equations it is found that in the slow rotation approximation charge accumulation not only acts like an additional mass, thus modifying the spherically symmetric part of the spacetime, the electric charge also contributes directly to the dragging of spacetime. A modified Lense-Thirring formula for the spacetime frame dragging frequency is obtained and its implication for rotating charged compact stars is discussed.     

Gravitational Deflection of Light in Rindler-Type Potential as a Possible Resolution to the Observations of Bullet Cluster 1E0657-558

The surface density Σ-map and the convergence κ-map of Bullet Cluster 1E0657-558 show that the center of baryonic matters separates from the center of gravitational force,and the distribution of gravitational force do not possess spherical symmetry.This hints that a modified gravity with difference to Newtonian inverse-square law at large scale,and less symmetry is worth investigating.In this paper,we study the dynamics in Randers-Finsler spacetime.The Newtonian limit and gravitational deflection of light in a Rindler-type potential is focused in particular.It is shown that the convergence in Finsler spacetime could account for the observations of Bullet Cluster.     

On quantum radiation in curved spacetime

In the context of quantum field theories in curved spacetime, we compute the effective action of the transition amplitude from vacuum to vacuum in the presence of an external gravitational field. The imaginary part of the resulted effective action determines the probability of vacuum decay via a quantum tunneling process, giving the rate and spectrum of particle creations. We show that (i) the gravitational field polarizes the vacuum and discretizes its spectrum; (ii) vacuum gains gravitational energy by such a polarization. On the basis of gravitational vacuum polarization, we discuss the quantum origin of vacuum decay in curved spacetime as pair-creations of particles and anti-particles. The thermal spectrum of particle creations is attributed to (i) the CPT invariance of pair-creations (annihilations) from (into) vacuum and (ii) vacuum acts as a reserve with the temperature determined by gravitational energy-gain.     

A new exact solution for colliding gravitational plane waves

A new exact solution of the vacuum Einstein equations describing the spacetime following the collision of two plane impulsive gravitational waves, each supporting a plane gravitational wave, is obtained. The solution has been extended prior to the instant of collision and the main features of the resulting space-time have been analyzed, using the Newman-Penrose formalism. It is shown that the result of the collision is the development of a singularity of the spacetime due to the simultaneous focussing of the two plane waves.     

Gravitational Perturbations of a Radiating Spacetime

This paper discusses the problem of gravitational perturbations of radiating spacetimes. We lay out the theoretical framework for describing the interaction of external gravitational fields with a radiating spacetime. This is done by deriving the field perturbation equations for a radiating metric. The equations are then specialized to a Vaidya spacetime. For the Hiscock ansatz of a linear mass model of a radiating blackhole the equations are found separable. Further, the resulting ordinary differential equations are found to admit analytic solutions. We obtain the solutions and discuss their characteristics.