Related papers: Point massive particle in General Relativity
McVittie's spacetime is a spherically symmetric solution to Einstein's equation with an energy-momentum tensor of a perfect fluid. It describes the external field of a single quasi-isolated object with vanishing electric charge and angular…
Using the Einstein gravitation theory (EGT) we calculate the Schwarzschild metric that is defined in the surrounding vacuum of a spherically symmetric mass distribution, not in rotation. The field equations of the EGT with this metric were…
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on…
We show a stability result for the Schwarzschild singularity (inside the black hole region) for the Einstein vacuum equations. The result is proven in the class of polarized axial symmetry, under perturbations of the Schwarzschild data…
Approximate solutions representing the gravitational-electrostatic balance of two arbitrary point sources in general relativity have led to contradictory arguments in the literature with respect to the condition of balance. Up to the…
Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. L\"u, A. Perkins, C. Pope, K. Stelle [Phys.Rev.Lett. 114 (2015), 171601]…
In this article I present a simple Newtonian heuristic for deriving a weak-field approximation for the spacetime geometry of a point particle. The heuristic is based on Newtonian gravity, the notion of local inertial frames [the Einstein…
In this paper we present the general spherically symmetric static solution to the vacuum equations of Cotton gravity. The obtained metric solution reveals the presence of singularities at the photosphere of a spherical source, which…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
We present a general solution of the Einstein gravitational field equations for the static spherically symmetric gravitational interior spacetime of an isotropic fluid sphere. The solution is obtained by transforming the pressure isotropy…
We solve the Einstein equations in the Randall-Sundrum framework with a static, spherically symmetric matter distribution on the {\it physical brane} and obtain an approximate expression for the gravitational field outside the source to…
In this paper two things are done. First, it is pointed out the existence of exact asymptotically flat, spherically symmetric black holes when a self interacting, minimally coupled scalar field is the source of the energy momentum of the…
We study spherically symmetric static solutions to the semi-classical Einstein equation sourced by the vacuum energy of quantum fields in the curved space-time of the same solution. We found solutions that are small deformations of the…
We analyze the static and spherically symmetric perfect fluid solutions of Einstein field equations inspired by the non commutative geometry. In the framework of the non commutative geometry this solution is interpreted as a mini black hole…
In a scalar-vector-gravity theory with the vector sector described by nonlinear electrodynamics, the field equations are integrated using the well-known gravitational decoupling method. The resulting spacetime corresponds to a spherically…
We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic…
In the present article we have obtained new set of exact solutions of Einstein field equations for anisotropic fluid spheres by using the Herrera et al.[1] algorithm. The anisotropic fluid solution so obtained join continuously to…
We study the exact solution of Einstein's field equations consisting of a ($n+2$)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density $\rho$ and thickness $d$, surrounded by two…
Every general relativity textbook emphasizes that coordinates have no physical meaning. Nevertheless, a coordinate choice must be made in order to carry out real calculations, and that choice can make the difference between a calculation…
Quadratic gravity constitutes a prototypical example of a perturbatively renormalizable quantum theory of the gravitational interactions. In this work, we construct the associated phase space of static, spherically symmetric, and…