Related papers: A technique for generating new solutions of Einste…
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…
Starting with any stationary axisymmetric vacuum metric, we build anisotropic fluids. With the help of the Ernst method, the basic equations are derived together with the expression for the energy-momentum tensor and with the equation of…
The equations of motion of massive particles in GR are completely determined by the field equation. We utilize the particular form of Einstein's field equation and propose for the $N$-body problem of the equations that are Lorentz invariant…
In this paper, we present new axisymmetric and reflection symmetric vacuum solutions to the Einstein field equations. They are obtained using the Hankel integral transform method and all three solutions exhibit naked singularities. Our…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
This paper generalizes two previously known techniques for generating minimally coupled Einstein-scalar field solutions in 4 dimensions; the Buchdahl and Fonarev transformations. By applying this solution generation technique, minimally…
It is shown that the vacuum Einstein equations for an arbitrary stationary axisymmetric space-time can be completely separated by re-formulating the Ernst equation and its associated linear system in terms of a non-autonomous…
Given asymptotically flat initial data on M^3 for the vacuum Einstein field equation, and given a bounded domain in M, we construct solutions of the vacuum constraint equations which agree with the original data inside the given domain, and…
We survey some results on scalar curvature and properties of solutions to the Einstein constraint equations. Topics include an extended discussion of asymptotically flat solutions to the constraint equations, including recent results on the…
We present a new generating algorithm to construct exact non static solutions of the Einstein field equations with two-dimensional inhomogeneity. Infinite dimensional families of $G_1$ inhomogeneous solutions with a self interacting scalar…
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…
This is the first in a series Of papers in which we initiate the study Of very rough solutions to the initial value problem for the Einstein Vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which…
It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a…
We describe a simple technique for generating solutions to the classical field equations for an arbitrary nonlinear sigma-model minimally coupled to gravity. The technique promotes an arbitrary solution to the coupled Einstein/Klein-Gordon…
We demonstrate how the Einstein's equations for the $D$-dimensional spherical gravity can be written in the covariant vector-like form. These equations reveal easily the causal structure of curved spherically symmetric manifolds and may…
The Ernst formulation of the Einstein equations is generalised to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary…
This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a…
This work derives the elements of classical Einstein Cartan theory (EC) from classical general relativity (GR) in two ways. (I) Derive discrete versions of torsion (translational holonomy) and the spin torsion field equation of EC from one…
We show that the effective field equations for a recently formulated polynomial affine model of gravity, in the sector of a torsion-free connection, accept general Einstein manifolds---with or without cosmological constant---as solutions.…
We show that a set of conformally invariant equations derived from the Fefferman-Graham tensor can be used to construct global solutions of the vacuum Einstein equations, in all even dimensions. This gives, in particular, a new, simple…