Related papers: Comparison of Vacuum Static Quadrupolar Metrics
1- It is shown that the upper bound for $\alpha$ in the general solutions of spherically symmetric vacuum field equations(gr-qc/9812081,$\Lambda$=0) is nearly 10^3.This has been obtained by comparing the theoretical prediction for bending…
We present a physically reasonable source for an static, axially--symmetric solution to the Einstein equations. Arguments are provided, supporting our belief that the exterior space--time produced by such source, describing a quadrupole…
Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric…
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…
We study a spherically symmetric setup consisting of a Schwarzschild metric as the background geometry in the framework of classical polymerization. This process is an extension of the polymeric representation of quantum mechanics in such a…
We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possess the following remarkable…
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In…
We study spherically symmetric configurations of the quadratic $f(R)$ gravity in the Einstein frame. In case of a purely gravitational system, we have determined the global qualitative behavior of the metric and the scalaron field for all…
The exact static spherically symmetric solutions for pure-aether theory and Einstein-aether theory are presented. It is shown that both theories can deliver the Schwarzschild metric, but only the Einstein-aether theory contains solutions…
We provide all basic equations and concepts required to carry out a general study on axially symmetric static sources. The Einstein equations and the conservation equations are written down for a general anisotropic static fluid endowed…
We investigate static and spherically symmetric vacuum solutions in the symmetric teleparallel $f(\mathbb{Q})$ modified theory of gravity. Starting from a recently proposed classification of affine connections compatible with both the…
We derive spherically symmetric solutions of the classical \lambda-R model, a minimal, anisotropic modification of general relativity with a preferred foliation and two local degrees of freedom. Starting from a 3 + 1 decomposition of the…
Axisymmetric Solutions of the vacuum Einstein equations are found in the Papapetrou-Weyl gauge. The solutions depend on two pairs of functionals, each pair of two functions depends on a different arbitrarily chosen function of one variable.…
We develop a new covariant formalism to treat spherically symmetric spacetimes in metric} f(R) theories of gravity. Using this formalism we derive the general equations for a static and spherically symmetric metric in a general…
f(Q) gravity is the extension of symmetric teleparallel general relativity (STGR), in which both curvature and torsion vanish, and gravity is attributed to nonmetricity. This work performs theoretical analyses of static and spherically…
The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is presented. The spacelike section of the class of metrics under consideration is a warped product of the real line with a nontrivial…
The purpose of this article is to compute the asymptotic charges of a vacuum solution to the Einstein field equations describing a naked singularity with a non-vanishing quadrupole moment, known in the literature as the Zipoy-Voorhees…
We analyze (the harmonic map representation of) static solutions of the Einstein Equations in dimension three from the point of view of comparison geometry. We find simple monotonic quantities capturing sharply the influence of the Lapse…
The exact axisymmetric and static solution of the Einstein equations coupled to axisymmetric and static gravitating scalar (or phantom) field is presented. The spacetimes modified by the scalar field are explicitly given for the so called…
A general formula for the metric as an explicit function of the generic energy-momentum tensor is given which satisfies static plane symmetric Einstein's equations with cosmological constant.In order to illustrate it, the solutions for the…