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The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled…
In an important series of articles published during the 70's, Krasi\'nski displayed a class of interior solutions of the Einstein field equations sourced by a stationary isentropic rotating cylinder of perfect fluid. However, these…
We construct models of static spherical distributions of perfect fluid in trace--free Einstein gravity theory. The equations governing the gravitational field are equivalent to the standard Einstein's equations however, their presentation…
In a recent series of papers new exact analytical solutions of the Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of different kinds of fluids have been displayed, [Phys. Rev. D {\bf…
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 study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres are composed of a perfect fluid with a charge distribution that creates a…
We prove the existence of a class of plane symmetric perfect-fluid cosmologies with a (-1/3, 2/3, 2/3) Kasner-like singularity. These solutions of the Einstein equations depend on two smooth functions of one space coordinate. They are…
Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. In particular, these include all the solutions of dust and…
Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav. {\bf 15}, 2397…
A model approach to the description of static stars filled with a charged Pascal perfect fluid within the framework of general relativity is investigated. The metric is written in Bondi's radiation coordinates. The gravitational equations…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
Using a multi domain spectral method, we investigate systematically the general-relativistic model for axisymmetric uniformly rotating, homogeneous fluid bodies generalizing the analytically known Maclaurin and Schwarzschild solutions.…
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…
We obtain a new class of rotating black holes for Einstein theory with perfect fluid source in (2+1) dimensions. We conclude that these black hole solutions only depend on variable angular velocity $m(r)$. Some examples of these black holes…
In this thesis four separate problems in general relativity are considered, divided into two separate themes: coordinate conditions and perfect fluid spheres. Regarding coordinate conditions we present a pedagogical discussion of how the…
We interpret the exact solutions previously obtained for spherically symmetric shells of liquid fluid in General Relativity in terms of the energies involved. We show that a certain parameter that was introduced into the solutions by the…
A large family of inhomogeneous non-static spherically symmetric solutions of the Einstein equation for null fluid in higher dimensions has been obtained. It encompasses higher dimensional versions of many previously known solutions such as…
Using the well-known ``displace, cut and reflect'' method used to generate disks from given solutions of Einstein field equations, we construct static disks made of perfect fluid based on vacuum Schwarzschild's solution in isotropic…
A new Lagrangian framework has recently been proposed to describe interactions between relativistic perfect fluids and scalar fields. In this paper we investigate the Einstein static universe in this new class of theories, which have been…
We present the Ernst potential and the line element of an exact solution of Einstein's vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass…