Related papers: Exact static solutions for fluid gravitating balls…
We present solution generating methods which allow to construct exact static solutions to the equations of four-dimensional Einstein-Maxwell-Dilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations,…
We investigate some exact static cylindrically symmetric solutions for a perfect fluid in the metric $f(R)$ theory of gravity. For this purpose, three different families of solutions are explored. We evaluate energy density, pressure, Ricci…
Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…
New exact solutions to the field equations in the Einstein--Gauss--Bonnet modified theory of gravity for a 5--dimensional spherically symmetric static distribution of a perfect fluid is obtained. The Frobenius method is used to obtain this…
We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such…
We investigate gravitational collapse of thick shell of fluid in the isotropic homogeneous universe without radiation described by the Einstein gravity with cosmological constant. We construct analytic solutions of this kind interpolating…
We present a time-dependent uniform-density interior Schwarzschild solution, an exact solution to the Einstein field equations. Our solution describes the collapse (or the time-reversed expansion) of an object from an infinite radius to an…
We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlev\`e-Gullstrand, and Schwarzschild coordinates, in which the aether is always comoving, and present both…
It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle.…
We obtain the Einstein-Maxwell equations for (2+1)-dimensional static space-time, which are invariant under the transformation $q_0=i\,q_2,q_2=i\,q_0,\alpha \rightleftharpoons \gamma$. It is shown that the magnetic solution obtained with…
We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to…
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.…
This study explores singularity-free solutions to the static, spherical symmetric Einstein equations with the standard Schwarzschild solution as a boundary condition. Imposing the absence of curvature singularities and requiring…
We provide a new class of exact solutions for the interior in (2 + 1) dimensional spacetime. The solutions obtained for the perfect fluid model both with and without cosmological constant ($\Lambda$) are found to be regular and singularity…
We derive a new class of exact solutions characterized by the Szekeres-Szafron metrics (of class I), admitting in general no isometries. The source is a fluid with viscosity but zero heat flux (adiabatic but irreversible evolution) whose…
If one assumes a particular form of non-minimal coupling, called the conformal coupling, of a perfect fluid with gravity in the fluid-gravity Lagrangian then one gets modified Einstein field equation. In the modified Einstein equation, the…
Einstein's equations in matter are gravitational analogues of Maxwell's equations in matter, providing an effective classical description of gravitational fields. We derive Einstein's equations in matter for relativistic fluids, and use…
Perfect-fluid, static, cylindrically symmetric solutions of Einstein's field equations are obtained for the equations of state $\rho+3p=0$ and $\rho=p$. In the former case, the density and the pressure turn out to be constant while in the…
The general exact solution of the Einstein-Dirac equations with cosmological constant in the homogeneous Riemannian space of the Bianchi 1 type is obtained.
In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known…