Related papers: Nonstandard general relativity II
We derive an asymptotic solution of the vacuum Einstein equations that describes the propagation and diffraction of a localized, large-amplitude, rapidly-varying gravitational wave. We compare and contrast the resulting theory of strongly…
The missing of a Keplerian fall-off in the observed galaxy rotation curves represents classical evidence for the existence of dark matter on galactic scales. There has been some recent activity concerning the potential of modelling galactic…
We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein's equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an…
The symmetry method is used to derive solutions of Einstein's equations for fluid spheres using an isotropic metric and a velocity four vector that is non-comoving. Initially the Lie, classical approach is used to review and provide a…
In addition to the second-order Einstein equations on four-dimensional homogeneous isotropic background universe filled with the single perfect fluid, we also derived the second-order perturbations of the continuity equation and the Euler…
Two classes of stationary axisymmetric solutions of Einstein's equations for isolated differentially rotating matter sources are presented. The asymptotic regime is extracted, with attention to quasilocal gravitational energy, shear and…
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…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
In a series of articles we describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
Einstein's equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the…
In this paper we construct negatively curved Einstein spaces describing gravitational waves having a solvegeometry wave-front (i.e., the wave-fronts are solvable Lie groups equipped with a left-invariant metric). Using the Einstein…
We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free non-linear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism,…
In this paper Einstein's field equations, for static spherically symmetric perfect fluid models with a linear barotropic equation of state, are recast into a 3-dimensional regular system of ordinary differential equations on a compact state…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by…