Related papers: General Solutions to Static Plane Symmetric Einste…
For any configuration of a static plane-symmetric distribution of matter along space-time, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as…
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…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…
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…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
We use the model approach to the description of spherical gravitating static fluid ball with an electric charge in general relativity. The metric is written in Bondi's coordinates. The total energy-momentum tensor (EMT) is chosen as a sum…
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…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
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…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
Within the framework of General Relativity a model approach to a description of spherical gravitating static fluid balls with an electric charge is considered. The metric interval is written in Bondi's radiation coordinates. The total…
Spherically symmetric static solutions of the Einstein equations with a positive cosmological constant for the energy-momentum tensor of a barotropic perfect fluid are governed by the Tolman-Oppenheimer-Volkoff-de Sitter equation. Existence…
Cosmological solutions of Einstein's equation for fluids with heat flow in a generalized Robertson-Walker metric are obtained, generalizing the results of Bergmann.
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 apply the energy-momentum tensor which is coordinate independent to calculate the energy content of the axisymmetric solutions. Our results are compared with what have been obtained before within the framework of Einstein general…
The Einstein equations for a plane-symmetric gravitational field coupled to an arbitrary nonlinear sigma model (NSM) are shown to be represented in the form of dynamical equations of a {\it generalized effective NSM}. The gravitational…
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 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…
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…
Various models are under consideration with metric type flat FRW whose energy-momentum tensor is described by a perfect fluid whose generic equation state and taking into account the conservation principle, but considering some of the…