Related papers: A general method for solving light-like geodesics
We introduce a new, physical-space-based method for deriving the precise leading-order late-time behaviour of solutions to geometric wave equations on asymptotically flat spacetime backgrounds and apply it to the setting of wave equations…
An approach is presented to address singularities in general relativity using a complex Riemannian spacetime extension. We demonstrate how this method can be applied to both black hole and cosmological singularities, specifically focusing…
An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…
We present a generalization and refinement of the Sachs-Wolfe technique which unifies many of the approaches taken to date and clarifies both the physical and the mathematical character of the method. We illustrate the formalism with a…
We describe a method to analyze causal geodesics in static and spherically symmetric spacetimes of Kerr-Schild form which, in particular, allows for a detailed study of the geodesics in the vicinity of the central singularity by means of a…
The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a…
Equations of geodesic deviation for the 3-dimensional and 4-dimensional Riemann spaces are discussed. Availability of wide classes of exact solutions of such equations, due to recent results for the matrix Schr\"odinger equation, is…
This work is devoted to a mathematical analysis of the distributional Schwarzschild geometry. The Schwarzschild solution is extended to include the singularity; the energy momentum tensor becomes a delta-distribution supported at r=0. Using…
Schwarzschild's solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein's theory of General Relativity. However, Schwarzschild's…
Kerr-Schild solutions to the vacuum Einstein equations are considered from the viewpoint of integral equations. We show that, for a class of Kerr-Schild fields, the stress-energy tensor can be regarded as a total divergence in Minkowski…
Godel-type metrics are introduced and used in producing charged dust solutions in various dimensions. The key ingredient is a (D-1)-dimensional Riemannian geometry which is then employed in constructing solutions to the Einstein-Maxwell…
It is proved in the manuscript that as long as the proper coordinate transformation is introduced,, the equations of geodetic lines described in curved space-time can be transformed into the dynamic equations in flat space-time, that is to…
We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime. The solutions are parameterized explicitly by constants of motion -- the energy, the angular momentum, and the Carter constant -- and initial…
The purpose of this study is the derivation of the equation of motion for particles and light in the spacetime of Reissner-Nordstr\"{o}m-(anti-)de Sitter black holes in the background of different kinds of regular and exotic matter fields.…
In this article we study the geodesic motion of test particles and light in the Einstein-Maxwell-Dilaton-Axion black hole spacetime. We derive the equations of motion and present their solutions in terms of the Weierstra{\ss} $\wp$-,…
Contents: 1) Introduction and a few excursions [A word on the role of explicit solutions in other parts of physics and astrophysics. Einstein's field equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter and anti-de…
The dynamics of the leading self-force (0SF) order, corresponding to the geodesic motion of a light body in the exact background of a heavy body, are explicitly derived for the first time using a flat space scattering amplitude-based…
Intrinsic time quantum geometrodynamics resolved `the problem of time' and bridged the deep divide between quantum mechanics and canonical quantum gravity with a Schrodinger equation which describes evolution in intrinsic time variable. In…
The gravitation equations of the general relativity, written for Riemannian space-time geometry, are extended to the case of arbitrary (non-Riemannian) space-time geometry. The obtained equations are written in terms of the world function…
This paper studies the geodesics connecting two time-like separated boundary points in asymptotically anti-de Sitter (AdS) spacetime. We find that in spherically symmetry Schwarzschild AdS black hole, smooth space-like geodesics can connect…