Related papers: Vacuum Solutions of Einstein's Equations in Parabo…
In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
According to Birkhoff's theorem the only spherically symmetric solution of the vacuum Einstein field equations is the Schwarzschild solution. Inspite of imposing asymptotically flatness and staticness as initial conditions we obtain that…
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
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 present new exact inhomogeneous vacuum cosmological solutions of Einstein's equations. They provide new information about the nature of general cosmological solutions to Einstein's equations.
New axisymmetric stationary solutions of the vacuum Einstein equations in five-dimensional asymptotically flat spacetimes are obtained by using solitonic solution-generating techniques. The new solutions are shown to be equivalent to the…
We solve the Einstein vacuum-equations for the case of static and axisymmetric solutions in a system of coordinates different from the Weyl standard one. We prove that there exists a class of solutions with the appropriate asymptotical…
An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
A new class of higher-dimensional exact solutions of Einstein's vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to…
We present a method for generating exact solutions of Einstein equations in vacuum using harmonic maps, when the spacetime possesses two commutating Killing vectors. This method consists in writing the axisymmetric stationry Einstein…
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…
All Lorentz invariant solutions of vacuum Einstein's equations are found. It is proved that these solutions describe space-times of constant curvature.
We construct a 4-parameter family of inhomogeneous cosmological models, which contains two recently derived 3-parameter families as special cases. The corresponding exact vacuum solution to Einstein's field equations is obtained with…
In this note we examine some recently proposed solutions of the linearized vacuum Einstein equations. We show that such solutions are {\it not} symmetries of the Einstein equations, because of a crucial integrability condition.
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…
In this work we intend to discuss the solitonic solutions of Einstein's field equations in vacuum by constructing the solution to N solitons and studying some aspects of it. In conclusion, it will be shown how the Kerr black hole can be…
In a previous work [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478] we constructed solutions to the Einstein vacuum equations in 3+1 dimensions which…
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…