Related papers: Finding and using exact solutions of the Einstein …
In this article we find the general, exact solution for the gravitational field equations for diagonal, vacuum, separable metrics. These are metrics each of whose terms can be separated into functions of each space-time variable separately.…
An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approximated by the Kasner map, which describes a succession of…
The nature of gravity is fundamental to our understanding of our own solar system, the galaxy and the structure and evolution of the Universe. Einstein's general theory of relativity is the standard model that is used for almost ninety…
Soon after he proposed three classic observational tests for the general theory of relativity, Einstein realised that a consistent description of the universe as a whole provided another important challenge for the theory. In this essay, we…
This year marks the hundredth anniversary of Einstein's 1915 landmark paper "Die Feldgleichungen der Gravitation" in which the field equations of general relativity were correctly formulated for the first time, thus rendering general…
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…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
The Einstein-scalar field theory can be used to model gravitational physics with scalar field matter sources. We discuss the initial value formulation of this field theory, and show that the ideas of Leray can be used to show that the…
We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the…
Exact time-dependent solutions of Einstein's gravitational field equation for a spherical mass moving with arbitrarily high constant velocity are derived and analyzed. The threshold conditions required for gravitational repulsion of…
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…
The pathways along which A. Einstein and D. Hilbert independently came to the gravitational field equations are traced. Some of the papers that assert a point of view on the history of the derivation of the gravitational field equations…
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…
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…
We review the physics at the end of the nineteenth century and summarize the process of the establishment of Special Relativity by Albert Einstein in brief. Following in the giant's footsteps, we outline the scientific method which helps to…
We are entering an era where the numerical construction of generic spacetimes is becoming a reality. The use of computer simulations, in principle, allows us to solve Einstein equations in their full generality and unravel important…
We present a simple technique for generating new solutions of Einstein's equations using such function transformations that leave the field equations in the Ernst form. In this context we recover all the known covariant transformations of…
New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these…
A general covariant extension of Einstein\'{}s field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector $Z_\mu$. Einstein's solutions…
A method of solving the Einstein equations with a scalar field is presented. It is applied to find higher dimensional vacuum metrics invariant under the group SO(n + 1) acting on n-dimensional spheres.