Related papers: A new class of plane symmetric solution
The gravitational properties of the {\em only} static plane-symmetric vacuum solution of Einstein's field equations without cosmological term (Taub's solution, for brevity) are presented: some already known properties (geodesics, weak field…
We discuss conformally flat plane wave solutions of Einstein equations depending on the plane wave phase $\xi=\omega\tau-{\bf qx}$, where $\tau$ is the conformal time. We show that ideal fluid Einstein equations and scalar fields with…
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…
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.…
Stationary perfect-fluid configurations of Einstein's theory of gravity are studied. It is assumed that the 4-velocity of the fluid is parallel to the stationary Killing field, and also that the norm and the twist potential of the…
We investigate solutions of Einstein field equations for the non-static spherically symmetric perfect fluid case using different equations of state. The properties of an exact spherically symmetric perfect fluid solutions are obtained which…
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…
An algorithm recently presented by Lake to obtain all static spherically symmetric perfect fluid solutions, is extended to the case of locally anisotropic fluids (principal stresses unequal). As expected, the new formalism requires the…
In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These…
In this article on the basis of a new definition of spacetime symmetry, which is in accordance with the symmetry of the curvature invariants, we investigate exact vacuum solutions of Einstein field equations corresponding to both static and…
We ask the following question: Of the exact solutions to Einstein's equations extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The candidate…
Static and spherically symmetric perfect fluid solutions of Einstein's field equations with cosmological constant are analysed. After showing existence and uniqueness of a regular solution at the centre the extension of this solution is…
Einstein's equations of General Relativity form a highly nonlinear system, so most exact solutions rely on symmetry assumptions. Spherically symmetric spacetimes have been particularly important, providing a tractable yet physically rich…
Einstein's field equations for stationary Bianchi type II models with a perfect fluid source are investigated. The field equations are rewritten as a system of autonomous first order differential equations. Dimensionless variables are…
In this work, we obtained exact solutions of Einstein's field equations for plane symmetric cosmological models by assuming that thy admit conformal motion. The space-time geometry of these solutions is found to be nonsingular, non-vacuum…
Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…
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…
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…
The Einstein equations with a positive cosmological constant are coupled to the pressureless perfect fluid matter in plane symmetry. Under suitable restrictions on the initial data, the resulting Einstein-dust system is proved to have a…
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…