It has been shown in the previous paper that the metric in the semiclassical region of the collapse spacetime is expressed purely kinematically through the Bondi charges. Here the Bondi charges are expressed through this metric by calculating the vacuum radiation against its background. The result is closed equations for the metric and the Bondi charges. Notably, there is a nonvanishing flux of...

In this paper, we evaluate energy and momentum density distributions for the Weyl metric by using the well-known prescriptions of Einstein, Landau-Lifshitz, Papaterou and Möller. The metric under consideration is the static axisymmetric vacuum solution to the Einstein field equations and one of the field equations represents the Laplace equation. Curzon metric is the special case of this spacet...

Here, we investigate the possible optical anisotropy of vacuum due to gravitational field. In doing this, we provide sufficient evidence from direct coordinate integration of the null-geodesic equations obtained from the Lagrangian method, as well as ray-tracing equations obtained from the Plebanski’s equivalent medium theory. All calculations are done for the Schwarzschild geometry, which resu...

If (M, g) is a Lorentz manifold and S a spacelike hypersurface, let h and k denote the induced metric and second fundamental form of S respectively. The mean curvature of S is the trace trhk. An interesting class of spacelike hypersurfaces are those whose mean curvature is constant (CMC hypersurfaces). The Lorentz manifolds of primary interest in the following are those which possess a compact ...

In the study of spherical degenerate stars such as neutron stars, general relativistic effects are incorporated by using Tolman-Oppenheimer-Volkoff equations to describe their interior spacetime. However, equation states employed in studies invariably computed flat We show that curved spacetime these depend explicitly on metric function. Further, we ignoring metric-dependent gravitational time ...

I study a stochastic approach for warm inflation considering back reaction of the metric with the fluctuations of matter field. This formalism takes into account the local inhomogeneities of the spacetime in a globally flat Friedmann Robertson Walker metric. The stochastic equations for the fluctuations of the matter field and metric are obtained. Finally, the dynamics for the amplitude of thes...

A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a natural meaning to the concepts of cosmic time, spacelike hypersurfaces and timelike or lightlike flows without assuming the notion of a background metric. The c...

A new 8-dimensional conformal gauging avoids the unphysical size change, third order gravitational field equations, and auxiliary fields that prevent taking the conformal group as a fundamental symmetry. We give the structure equations, gauge transformations and intrinsic metric structure for the new biconformal spaces. We prove that a torsion-free biconformal space with exact Weyl form, closed...

The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, a...