Related papers: Point massive particle in General Relativity
Translation by S. Antoci and A. Loinger of the fundamental memoir, that contains the ORIGINAL form of the solution of Schwarzschild's problem. The solution is regular in the whole space-time, with the only exception of the origin of the…
Exact time-dependent solutions of Einstein's gravitational field equation for a spherical mass moving with arbitrarily high constant velocity are derived and analyzed. The threshold conditions required for gravitational repulsion of…
In this article we investigate the properties of the asymptotically Schwarzschild-like metric as an alternative to the Schwarzschild solution in General Relativity. While asymptotically flat and similar to Schwarzschild at large distances…
The Schwarzschild metric is derived in a manner that does not require familiarity with the formalism of differential geometry beyond the ability to interpret a general spacetime metric. As such, the derivation is suitable for an…
The geodesic equations for the general case of diagonal metrics of static, spherically symmetric fields are calculated. The elimination of the proper time variable gives the motion equations for test particles with respect to coordinate…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
We study a static spherically symmetric problem with a black hole and radially directed geodesic flows of dark matter. The obtained solutions have the following properties. At large distances, the gravitational field produces constant…
In Einstein's theory of general relativity the vacuum solution yields a blackhole with a curvature singularity, where there exists a point-like source with a Dirac delta distribution which is introduced as a boundary condition in the static…
We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with…
We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free non-linear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism,…
Solutions of Einstein vacuum equations, for a static pseudospherically symmetric system, are presented. They describe a naked singularity and a singular solution with many resemblances to the Schwartzschild solution but with two major…
According to the Einstein hole argument, vacuum metric solutions are equivalent only if they correspond to the same energy--momentum tensor in the source region. In this paper it is shown that singular coordinates that are used to show…
The present work describes an immersion in 5D of the interior Schwarzschild solution of the general relativity equations. The model theory is defined in the context of a flat 5D space time matter Minkowski model, using a Tolman like…
We present a method for computing the evolution of a spacetime containing a massive particle and a black hole. The essential idea is that the gravitational field is evolved using full numerical relativity, with the particle generating a…
The Kaluza-Klein formalism of the Einstein's theory, based on the (2,2)-fibration of a generic 4-dimensional spacetime, describes general relativity as a Yang-Mills gauge theory on the 2-dimensional base manifold, where the local gauge…
We present a stationary spherically symmetric solution of the Einstein equations, with a source generated by a scalar field of $q$-theory. In this theory Riemannian gravity, as described by the Einstein - Hilbert action, is coupled to a…
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…
We construct spherically symmetric, static solutions to the Einstein-Vlasov system with non-vanishing cosmological constant $\Lambda$. The results are divided as follows. For small $\Lambda>0$ we show existence of globally regular solutions…
We study static spherically symmetric solutions to the vacuum field equations of quadratic gravity in the presence of a cosmological constant $\Lambda$. Motivated by the trace no-hair theorem, we assume the Ricci scalar to be constant…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…