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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…
We present a general method to obtain static anisotropic spherically symmetric solutions, satisfying a nonlocal equation of state, from known density profiles. This equation of state describes, at a given point, the components of the…
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…
This study explores singularity-free solutions to the static, spherical symmetric Einstein equations with the standard Schwarzschild solution as a boundary condition. Imposing the absence of curvature singularities and requiring…
We construct the general spherically symmetric and self-similar solution of the Einstein-Vlasov system (collisionless matter coupled to general relativity) with massless particles, under certain regularity conditions. Such solutions have a…
We derive the general solution to the coupled Einstein and Dirac field equations in static and hyperplane-symmetric spacetime of arbitrary dimension including a cosmological constant of either sign. As a result, only a massful Dirac field…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
The Vlasov-Einstein system describes the evolution of an ensemble of particles (such as stars in a galaxy, galaxies in a galaxy cluster etc.) interacting only by the gravitational field which they create collectively and which obeys…
The spherically symmetric solution for perfect fluid with homogeneous density and inhomogeneous pressure has been considered. This solution is known as Stephani solution. The matching of this solution and de Sitter solution has been done on…
Exact solutions of the Einstein's field equations describing a spherically symmetric cosmological model without a big bang or any other kind of singularity recently obtained by Dadhich and Patel (2000) are revisited. The matter content of…
The paper is concerned with the Einstein equations for a spherically symmetric static distribution of anisotropic matter. The equations are cast into a system of Fuchsian type ODE for certain scalar invariants of the strain. And then the…
Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations.…
I use the Newtonian equation of hydrostatic equilibrium for an isotropic fluid sphere to generate exact anisotropic solutions of Einstein's equations. The input function is simply the density. An infinite number of regular solutions are…
In this paper we investigate a class of solutions of Einstein equations for the plane-symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the…
In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between…
We explore some of the gravitational features of a uniform ring both in the Newtonian potential theory and in General Relativity. We use a spacetime associated to a Weyl static solution of the vacuum Einstein's equations with ring like…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
In this article, an exact solution of Einstein's field equations for spherically symmetric anisotropic matter distributions in isotropic coordinates is obtained. For this, the solution has been obtained by using a generalized physically…
A procedure to find static axially symmetric solutions to the Einstein field equations is presented. We obtained two general solutions and five particular solutions, which depend on the existence conditions for circular and $z$ direction…
A spherically symmetric charged ideal fluid solution of Einstein field equation is given in the presence of the cosmological constant and two well known example of this type of solution is presented. If the matter is confined in a region,…