Related papers: Axisymmetric Stationary Solutions as Harmonic Maps
We study how the changes of coordinates between the class of harmonic coordinates affect the analitycal solutions of Einstein's equations and we apply it to an analytical approach for stationary and axisymmetric solutions of Einstein…
The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled…
In this work, we introduce a method for finding exact solutions to the vacuum Einstein field equations in higher dimensions from a given solution to the chiral equation. When considering a $n + 2$-dimensional spacetime with $n$ commutative…
In a space-time $M$ with a Killing vector field $\xi^a$ which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of $\xi^a$ gives a 3-dimension space $S$. Besides the symmetry-reduced action from that…
This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such…
We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry,…
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…
We construct two classes of exact solutions to six and higher dimensional Einstein-Maxwell theory in which the metric functions can be written as convolution-like integrals of two special functions. The solutions are regular everywhere and…
A new solution to the Einstein-Maxwell field equations is presented describing a cylindrically symmetric homogeneous cosmology. The solution is conformally flat, it possesses seven Killing vectors of which the timelike one is rotating and…
In recent works we have constructed axisymmetric solutions to the Euler-Poisson equations which give mathematical models of slowly uniformly rotating gaseous stars. We try to extend this result to the study of solutions of the…
In this article we make a thorough classification of (not necessarily complete) $n$-dimensional vacuum static spaces $(M,g,f)$ with harmonic curvature and, as a corollary, obtain a classification of complete vacuum static spaces with…
In this paper we construct a special class of four dimensional axisymmetric stationary spacetimes whose Ricci scalar is constant but not Einstein. We find that this solution has a ring singularity. At the end, we discuss some numerical…
We present a method for generating exact interior solutions of Einstein's equations in the case of static and axially symmetric perfect-fluid spacetimes. The method is based upon a transformation that involves the metric functions as well…
The conditions for the existence of Killing-Yano tensors, which are closely related to the appearance of non-generic world-line SUSY, are presented for static axisymmetric spacetimes. Imposing the vacuum Einstein equation, the set of…
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…
The Einstein equations for a plane-symmetric gravitational field coupled to an arbitrary nonlinear sigma model (NSM) are shown to be represented in the form of dynamical equations of a {\it generalized effective NSM}. The gravitational…
Lying at the intersection of Ado's theorem and the Nash embedding theorem, we consider the problem of finding faithful representations of Lie groups which are simultaneously isometric embeddings. Such special maps are found for a certain…
We investigate static axially symmetric black hole solutions in a four-dimensional Einstein-Yang-Mills-SU(2) theory with a negative cosmological constant $\Lambda$. These solutions approach asymptotically the anti-de Sitter spacetime and…
We start a systematic investigation of possible isometries of the asymptotically de Sitter solutions to Einstein equations. We reformulate the Killing equation as conformal equations for the initial data at $\mathcal{I}^+$. This allows for…
Here I present a stationary cylindrically symmetric asymptotically Einstein static universe solution with the matter consisting of a cosmological and rotating dust term which admits predicted black hole event horizon.