Related papers: Static solutions from the point of view of compari…
A black hole solution in a teleparallel theory of (2+1)-dimensional gravity, given in a previous paper, is examined. This solution is also a solution of the three-dimensional vacuum Einstein equation with a vanishing cosmological constant.…
The assumption that a solution to the Einstein equations is static (or stationary) very strongly constrains the asymptotic behaviour of the metric. It is shown that one need only impose very weak differentiability and decay conditions {\it…
We get the general static, spherically symmetric solutions of the d-dimensional Einstein-Maxwell-Dilaton theories by dimensionally reducing them to a class of 2-dimensional dilaton gravity theories. By studying the symmetries of the actions…
In this paper, we present two observations about static spherically symmetric solutions of the Einstein-Klein-Gordon equations. The first is a comment extending the well-known result of the existence of static states (i.e. standing wave…
In this paper, we investigate the numerical solutions for spherically symmetric situations in Einstein cubic gravity. In addition to the previously found black hole solutions, we uncover a new class of solutions that lack horizons. Due to…
We investigate circularly symmetric static solutions in three-dimensional gravity with a minimally coupled massive scalar field. We integrate numerically the field equations assuming asymptotic flatness, where black holes do not exist and a…
We present a detailed analysis of the general exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with density proportional to pressure. We study the geodesics in it and we show that…
We present a simple and complete classification of static solutions in the Einstein-Maxwell system with a massless scalar field in arbitrary $n(\ge 3)$ dimensions. We consider spacetimes which correspond to a warped product $M^2 \times…
In this paper, we address the issue of linear stability of Schwarzschild space- time subject to certain axisymmetric perturbations. In particular, we prove that associ- ated solutions to the linearized vacuum Einstein equations centered at…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
Numerical solutions to the Einstein constraint equations are constructed on a selection of compact orientable three-dimensional manifolds with non-trivial topologies. A simple constant mean curvature solution and a somewhat more complicated…
We establish mass lower bounds of Penrose-type in the setting of $3$-dimensional initial data sets for the Einstein equations satisfying the dominant energy condition, which are either asymptotically flat or asymptotically hyperboloidal.…
The spherically symmetric perturbations in the spatially flat Friedman models are considered. It is assumed that the Friedmannian density and pressure are related through a linear equation of state. The perturbation is joined smoothly with…
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…
We study the perturbations of two classes of static black ellipsoid solutions of four dimensional vacuum Einstein equations. Such solutions are described by generic off--diagonal metrics which are generated by anholonomic transforms of…
By applying the method of moving frames modelling one and two dimensional local anisotropies we construct new solutions of Einstein equations on pseudo-Riemannian spacetimes. The first class of solutions describes non-trivial deformations…
We present a symmetric hyperbolic formulation of the Einstein equations in affine-null coordinates. Giannakopoulos et. al. (arXiv:2007.06419) recently showed that the most commonly numerically implemented formulations of the Einstein…
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…
We study isometric embeddings of some solutions of the Einstein equations with suffciently high symmetries into a flat ambient space. We briefly describe a method for constructing surfaces with a given symmetry. We discuss all minimal…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…