Related papers: Static plane symmetric relativistic fluids and emp…
We obtain Vaidya-like solutions to include both a null fluid and a string fluid in non-spherical (plane symmetric and cylindrical symmetric) anti-de Sitter space-times. Assuming that string fluid diffuse, we find exact solutions of…
Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial…
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…
We consider the Einstein equations coupled to an ultrastiff perfect fluid and prove the existence of a family of solutions with an initial singularity whose structure is that of explicit isotropic models. This family of solutions is…
In the present work, we execute the Lie symmetry analysis on the Einstein-Maxwell field equations in the plane symmetric spacetime. Under the background of the plane symmetric space-time we compute the Lie point symmetries, perform the…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…
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…
Disks of collisionless particles are important models for certain galaxies and accretion disks in astrophysics. We present here a solution to the stationary axisymmetric Einstein equations which represents an infinitesimally thin dust disk…
We obtain an exact solution for the Einstein's equations with cosmological constant coupled to a scalar, static particle in static, "spherically" symmetric background in 2+1 dimensions.
Exact non-static spherically symmetric solutions of the Einstein equations for a null fluid source with pressure $P$ and density $\rho$ related by $P = k\rho^a$ are given. The $a=1$ metrics are asymptotically flat for $1/2<k\le 1$ and…
Streamlines of a relativistic perfect isentropic fluid are geodesics of a Riemannian space whose metric is defined by enthalpy of the fluid. This fact simplifies the solution of some problems, as is also of interest from the point of view…
Static spherically symmetric solution of the Einstein's equations is found representing averaged properties of an infinite self-gravitating gas in the dynamical equilibrium. It depends upon three parameters: the core radius, the…
The spherically symmetric perturbations in the spatially flat Friedman models are considered. It is assumed that the Friedmannian density and pressure are related through a linear equation of state. The perturbation is joined smoothly with…
The properties of LRS class II perfect fluid space-times are analyzed using the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives. In this manner it is straightforward to obtain the…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…
We consider Einstein's equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data,…
It is proved that the only geodesically complete stationary vacuum solution of the Einstein equations is the empty Minkowski space, or a quotient of it by a discrete group of isometries, generalizing a classical result of Lichnerowicz. In…
The full set of equations governing the structure and the evolution of self--gravitating cylindrically symmetric dissipative fluids with anisotropic stresses, is written down in terms of scalar quantities obtained from the orthogonal…