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In this paper we present Plane symmetric, Cylindrically Symmetric and Spherically Symmetric Black hole or Vacuum solutions of Einstein Field Equations(EFEs). Some of these solutions are new which we have not seen in the literature. This…
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.…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
We consider Einstein's equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data,…
Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear…
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 discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…
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…
We study massless solutions to the Einstein equations coupled to different matter models with a magnetic field and a conformal gauge singularity assuming spatial homogeneity with three commuting spatial translations. We show that there are…
The special conformal transformation (composed by inversion - translation - inversion) is used to generate a time dependent conformally flat spacetime. In order to be an exact solution of Einstein's equations, we need as a source a stress…
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…
In this paper, we study new exact solutions of Einstein's field equations with the motivation of the relativistic elasticity theory. We construct the static conformal elastic solution by applying conformal transformations to the…
We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type…
We obtain a two-parameter set of solutions, which represents a spherically symmetric space-time with a superposition of a neutral fluid and an electric field. The electromagnetic four-potential of this Einstein-Maxwell space-time is taken…
The problem is solved of describing scale factors of a homogeneous isotropic spaces-time such that the exact solution for the scalar field with a nonconformal coupling to curvature can be obtained from solutions for the conformally coupled…
An exact plane-symmetric non-stationary solution to the Einstein-Maxwell equations for a magnetoactive plasma is obtained and studied.
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 determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
A new class of plane symmetric solution sourced by a perfect fluid is found in our recent work. An n-dimensional ($n\geq 4$) global plane symmetric solution of Einstein field equation generated by a perfect fluid source is investigated,…