Related papers: A technique for generating new solutions of Einste…
A solution of the Einstein vacuum field equations is constructed within the contex of perturbation theory. The solution possesses a graphical representation in terms of diagrams.
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…
A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the…
We generate an explicit four-fold infinity of physically acceptable exact perfect fluid solutions of Einstein's equations by way of conformal transformations of physically unacceptable solutions (one way to view the use of isotropic…
We present a method for constructing stationary, asymptotically flat, rotating solutions of Einstein's field equations. One of the spun-up solutions has quasilocal mass but no global mass. It has an ergosphere but no event horizon. The…
We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and…
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…
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…
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…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear…
More than thirty years passed since the first discoveries of various aspects of integrability of the symmetry reduced vacuum Einstein equations and electrovacuum Einstein - Maxwell equations were made and gave rise to constructions of…
We apply the method of B\"acklund transformations to generate a new hierarchy of exact solutions to the vacuum Einstein equations starting from the extreme Kerr near-horizon geometry. Solutions with extreme Kerr near-horizon asymptotics…
A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by…
We employ the gravitational decoupling approach for static and spherically symmetric systems to develop a simple and powerful method in order to a) continuously isotropize any anisotropic solution of the Einstein field equations, and b)…
A new solution of Einstein's vacuum field equations is discovered which appears as a generalization of the well-known Ozsvath-Schucking solution and explains its source of curvature which has otherwise remained hidden. Curiously, the new…
Complete sequences of new analytic solutions of Einstein's equations which describe thin super massive disks are constructed. These solutions are derived geometrically. The identification of points across two symmetrical cuts through a…
A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using…
This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…
The aim of this article is to construct initial data for the Einstein equations on manifolds of the form R n+1 x T m , which are asymptotically flat at infinity, without assuming any symmetry condition in the compact direction. We use the…
The first step in the building of a spacetime solution of Einstein's gravitational field equations via the initial value formulation is finding a solution of the Einstein constraint equations. We recall the conformal method for constructing…