Related papers: Some exact solutions in general relativity
We exhibit a simple and explicit formula for the metric of an arbitrary static spherically symmetric perfect fluid spacetime. This class of metrics depends on one freely specifiable monotone non-increasing generating function. We also…
We solve the Einstein constraint equations for a first-order causal viscous relativistic hydrodynamic theory in the case of a conformal fluid. For such a theory, a direct application of the conformal method does not lead to a decoupling of…
Two new classes of exact interior static solutions of the Einstein equations in homogeneous coordinates for a gravitating ball filled by a Pascal perfect fluid are obtained. Schwarzschild's interior solution of is a special case of these…
Rainich-type conditions giving a spacetime "geometrization" of matter fields in general relativity are reviewed and extended. Three types of matter are considered: perfect fluids, scalar fields, and electromagnetic fields. Necessary and…
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 express Einstein's field equations for a spherically symmetric ball of general fluid such that they are conducive to an initial value problem. We show how the equations reduce to the Vaidya spacetime in a non-null coordinate frame,…
In this thesis, we consider two different problems relevant to general relativity. Over the last few years, opinions on physically relevant singularities occurring in FRW cosmologies have considerably changed. We present an extensive…
We derive the covariant optimality conditions for rocket trajectories in general relativity, with and without a bound on the magnitude of the proper acceleration. The resulting theory is then applied to solve two specific problems: the…
We investigate an exact solution that describes the embedding of the four-dimensional (4D) perfect fluid in a five-dimensional (5D) Einstein spacetime. The effective metric of the 4D perfect fluid as a hypersurface with induced matter is…
The system consisting of a self gravitating perfect fluid and scalar field is considered in detail. The scalar fields considered are the quintessence and ``tachyonic'' forms which have important application in cosmology. Mathematical…
In this work, we derive the general solutions for a cylindrically symmetric space-time filled with a cosmological perfect fluid obeying $p=\gamma \rho$ ($0\leq \gamma \leq 1$), where $\gamma=1$ represents a stiff or Zeldovich fluid. Using…
We apply the 1+1+2 covariant semi-tetrad approach to describe a general static and spherically symmetric relativistic stellar object which contains two fluids with anisotropic pressure. The corresponding Tolman-Oppenheimer-Volkoff equations…
We find the general behaviour of homogeneous and isotropic cosmological models in some fourth-order theories of gravity. Explicit, exact, general solutions are given for both empty universes and those filled with a perfect fluid. For the…
Despite the fact that the Schwarzschild and Kerr solutions for the Einstein equations, when written in standard Schwarzschild and Boyer-Lindquist coordinates, present coordinate singularities, all numerical studies of accretion flows onto…
We consider anisotropic fluids with directional pressures $p_i = w_i \rho$ ($\rho$ is the density, $w_i = $const, $i = 1,2,3$) as sources of gravity in stationary cylindrically symmetric space-times. We describe a general way of obtaining…
Gravity is a phenomenon which arises due to the space-time geometry. The main equations that describe gravity are the Einstein equations. To understand the consequences of these field equations we need to calculate the free particle…
In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between…
We study spherically symmetric static spacetimes generally filled with an anisotropic fluid in the nonrelativistic general covariant theory of gravity. In particular, we find that the vacuum solutions are not unique, and can be expressed in…
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 consider self-gravitating fluids in cosmological spacetimes with Gowdy symmetry on the torus $T^3$ and, in this class, we solve the singular initial value problem for the Einstein-Euler system of general relativity, when an initial data…