Related papers: Generating static perfect-fluid solutions of Einst…
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…
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…
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 explicit necessary condition for the occurrence of resonance scattering of axial gravitational waves, along with the internal trapping of null geodesics, is proposed for static spherically symmetric perfect fluid solutions to Einstein's…
We present a new generating algorithm to construct exact non static solutions of the Einstein field equations with two-dimensional inhomogeneity. Infinite dimensional families of $G_1$ inhomogeneous solutions with a self interacting scalar…
I present a new method to generate rotating solutions of the Einstein--Maxwell equations from static solutions, and briefly discuss its general properties.
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…
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…
We study the Einstein equations of the static spherically symmetric anisotropic fluid system in curvature coordinates to find algorithms that generate all solutions and all solutions that are regular at the center. All possible combinations…
In this work we propose a new procedure for to extract global information of a space-time. We considered a space-time immersed in a higher dimensional space and we formulate the equations of Einstein through of the Frobenius conditions to…
We modify the method to generate the exact solutions of the Einstein equations basing on the laws of thermodynamics. Firstly, the Komar mass is used to take the place of the Misner-Sharp energy which is used in the original methods, and…
Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
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 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…
An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the…
The Kerr solution for empty space-time is presented in an ellipsoidally symmetric coordinate system and it is used to produce generalised ellipsoidal metrics appropriate for the generation of rotating interior solutions of Einstein's…
A new class of static plane symmetric solution of Einstein field equation generated by a perfect fluid source is put forward. A special family of this new solution is investigated in detail. The constraints on the parameters by different…
The properties of a transformation previously considered for generating new perfect-fluid solutions from known ones are further investigated. It is assumed that the four-velocity of the fluid is parallel to the stationary Killing field, and…
We introduce a physical characterization of the static and stationary perfect fluid solutions of the Einstein field equations with a single or 2-component perfect fluid sources, according to their gravitoelectric and gravitomagnetic fields.…
In a recent series of papers new exact analytical solutions of Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. We have first considered a fluid with an…