Related papers: A rotating three component perfect fluid source an…
In a recent series of papers, new exact analytical solutions to field equations of General Relativity representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids with various equations of state have been…
A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $\Lambda$ and null fluid) in $2+1$ dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For…
We present a method for generating exact interior solutions of Einstein's equations in the case of static and axially symmetric perfect-fluid spacetimes. The method is based upon a transformation that involves the metric functions as well…
A double new class of solutions to the general relativity field equations describing interior spacetimes sourced by stationary cylindrical anisotropic fluids with principal stress directed along the symmetry axis is displayed. 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…
Einstein's equations for a Robertson-Walker fluid source endowed with rotation Einstein's equations for a Robertson-Walker fluid source endowed with rotation are presented upto and including quadratic terms in angular velocity parameter. A…
We present stationary and axially-symmetric black hole solutions to the Einstein field equations sourced by an anisotropic fluid, describing rotating black holes embedded in astrophysical environments. We compute their physical properties,…
In this note the Schwarzschild and Kerr solutions are constructed for 3 space and $N$ time dimensions. Solutions, by construction, possesses symmetry with respect to rotations in time volume.
Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric…
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…
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…
Instead of conformal to flat spacetime, we take the metric conformal to a spacetime which can be thought of as ``minimally'' curved in the sense that free particles experience no gravitational force yet it has non-zero curvature. The base…
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…
Starting with generic stationary axially symmetric spacetimes depending on two spacelike isotropic orthogonal coordinates $x^{1}, x^{2}$, we build anisotropic fluids with and without heat flow but with wanishing viscosity. In the first part…
A spacetime endowed with an anisotropic fluid is proposed for the interior of a Schwarzschild black hole. The geometry has an instantaneous Minkowski form and is a solution of Einstein's equations with a stress tensor on the r.h.s. obeying…
Axially symmetric stationary metrics governed by the Einstein-Euler equations for slowly rotating perfect fluids have been constructed in an arbitrarily large bounded domain containing the support of the mass density. However the problem of…
A new class of exact spacetimes in Einstein's gravity, which are Kerr black holes immersed in an external magnetic (or electric) field that is asymptotically uniform and oriented along the rotational axis, is presented. These are…
We consider the extension of the Majumdar-type class of static solutions for the Einstein-Maxwell equations, proposed by Ida to include charged perfect fluid sources. We impose the equation of state $\rho+3p=0$ and discuss spherically…
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…
The symmetry method is used to derive solutions of Einstein's equations for fluid spheres using an isotropic metric and a velocity four vector that is non-comoving. Initially the Lie, classical approach is used to review and provide a…