Related papers: Approximate perfect fluid solutions with quadrupol…
We consider the 3-dimensional formulation of Einstein's theory for spacetimes possessing a non-null Killing field $\xi^a$. It is known that for the vacuum case some of the basic field equations are deducible from the others. It will be…
We reduce Einstein's field equations for the interior of a uniformly rotating, axisymmetric perfect fluid to a system of six second order partial differential equations for the pressure p the energy density $\mu$ and four dependent…
In a recent series of papers new exact analytical interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. A fluid with an axially directed pressure has been first considered, then a perfect fluid,…
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…
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…
In this article, a cylindrical symmetry and static solution of the Einstein's field equations, was presented. The space-time is conformally flat, regular everywhere except on the symmetry axis where it possesses a naked curvature…
We generate an explicit four-fold infinity of physically acceptable exact perfect fluid solutions of Einstein's equations by way of conformal transformations of physically unacceptable solutions (one way to view the use of isotropic…
A, recently presented, general procedure to find static and axially symmetric, interior solutions to the Einstein equations, is extended to the stationary case, and applied to find an interior solution for the Kerr metric. The solution,…
The structure of the Einstein field equations describing the gravitational collapse of spherically symmetric isotropic fluids is analyzed here for general equations of state. A suitable system of coordinates is constructed which allows us,…
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…
Using an orthonormal Lorentz frame approach to axistationary perfect fluid spacetimes, we have formulated the necessary and sufficient equations as a first order system, and investigated the integrability conditions of this set of…
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…
Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary…
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…
This diploma thesis analyses static, spherically symmetric perfect fluid solutions to Einstein's field equations with cosmological constant. Constant density solutions are derived for different values of the cosmological constant. Eleven…
We present a physically reasonable source for an static, axially--symmetric solution to the Einstein equations. Arguments are provided, supporting our belief that the exterior space--time produced by such source, describing a quadrupole…
Applying the method of conformal metric to a given static axially symmetric vacuum solution of the Einstein equations, we have shown that there is no solution representing a cosmic ideal fluid which is asymtotically FLRW. Letting the cosmic…
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…
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on…
An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect fluid solutions of Einstein's equations. For physically relevant…