Related papers: Curious interior solutions of general relativity
We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…
The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness…
We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic…
We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the…
We present a method for generating exact interior solutions of Einstein's equations in the case of static and axially symmetric perfect-fluid spacetimes. The method is based upon a transformation that involves the metric functions as well…
In this paper, we present a formalism to generate a family of interior solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner-Nordstr\"om…
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…
Starting from the solution of the Einstein field equations in a static and spherically symmetric spacetime which contains an isotropic fluid, we construct a model to represent the interior of compact objects with compactness rate…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…
When solving the equations of General Relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress-energy. This implies that for static and isotropic spacetimes, the most general natural…
An exact solution of the Einstein field equations is proposed which represents a differentially rotating fluid. As this solution matches the exterior Kerr solution and reduces to the Schwarzschild interior solution by setting the rotational…
In this article on the basis of a new definition of spacetime symmetry, which is in accordance with the symmetry of the curvature invariants, we investigate exact vacuum solutions of Einstein field equations corresponding to both static and…
We solve the Einstein vacuum-equations for the case of static and axisymmetric solutions in a system of coordinates different from the Weyl standard one. We prove that there exists a class of solutions with the appropriate asymptotical…
In this work we present an approximate solution of the Einstein equations describing a global model for the gravitational field generated by a bounded, self-gravitating stationary and axisymmetric body rotating rigidly with constant angular…
Axisymmetric Solutions of the vacuum Einstein equations are found in the Papapetrou-Weyl gauge. The solutions depend on two pairs of functionals, each pair of two functions depends on a different arbitrarily chosen function of one variable.…
Here we describe a stationary cylindrically symmetric solution of Einstein's equation with matter consisting of a positive cosmological and rotating dust term. The solution approaches Einstein static universe solution.
A class of gauges for the Einstein vacuum equations is introduced, along with three symmetric hyperbolic systems. The first implies the local realizability of the gauge. The second is the dynamical subset of the field equations. The third…
The general solution of the system of General Relativity equations has been found for isotropic Universe with the flat spatial distribution and synchronized time taking into account a perfect dust and the cosmological constant.…
Rastall's theory belongs to the class of non-conservative theories of gravity. In vacuum, the only non-trivial static, spherically symmetric solution is the Schwarzschild one, except in a very special case. When a canonical scalar field is…
In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…