Related papers: Solutions of the Einstein equations with matter
In contrast to electrodynamics, Einstein's gravitation equations are not invariant with respect to a wide class of the mapping of field variables which leave equations of motion of test particles in a given coordinate system invariant. It…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…
The theoretical description of compact structures that share some key features with mass varying particles allows for a simple analysis of equilibrium and stability for massive stellar bodies. We investigate static, spherically symmetric…
We present new exact solutions for the Einstein-Maxwell system in static spherically symmetric interior spacetimes. For a particular form of the gravitational potentials and the electric field intensity, it is possible to integrate the…
We attempt to see how closely we can formally obtain the planetary and light path equations of General Relativity by employing certain operations on the familiar Newtonian equation. This article is intended neither as an alternative to nor…
We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
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…
A new class of solutions to Einstein's classical field equations of general relativity is presented. The solutions describe a non-rotating, spherically symmetric, compact self gravitating object, residing in a static electro-vacuum space…
We study the non-relativistic expansion of general relativity coupled to matter. This is done by expanding the metric and matter fields analytically in powers of $1/c^2$ where $c$ is the speed of light. In order to perform this expansion it…
The "Newtonian" or non-relativistic decomposition of Einstein's gravitational field is useful in the post-Newtonian approximation. We obtain the full non-quadratic Einstein-Hilbert action in terms of these fields as well as the harmonic…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…
We submit the viewpoint that, perhaps, some of the controversies in gravitation occurred during this century are not due to insufficiencies of Einstein's field equations, but rather to insufficiencies in the mathematics used for their…
We try to lay down the foundations of a Newtonian theory where inertia and gravitational fields appear in a unified way aiming to reach a better understanding of the general relativistic theory. We also formulate a kind of equivalence…
Several attempts to construct theories of gravity with variable mass are considered. The theoretical impacts of allowing the rest mass to vary with respect to time or an appropriate curve parameter are examined in the framework of Newtonian…
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for…
We investigate the vacuum and charged spherically symmetric static solutions of the Einstein equations on cosmological background. The background metric is not flat, but curved, with constant - curvature spatial sections. Both vacuum and…
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations…
The Einstein postulates assert an invariance of the propagation speed of light in vacuum for any observer, and which amounts to a presumed absence of any preferred frame. The postulates appear to be directly linked to relativistic effects…
Attempts to merge Einsteinian gravity with Newtonian run into inconsistencies because in Newton's gravity time is absolute and the speed of gravity is infinite. Such an assumption was in a focus of attention of scientists in 19th century…