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The qualitative properties of spatially homogeneous stiff perfect fluid and minimally coupled massless scalar field models within general relativity are discussed. Consequently, by exploiting the formal equivalence under conformal…
A representation of spatial infinity based in the properties of conformal geodesics is used to obtain asymptotic expansions of the gravitational field near the region where null infinity touches spatial infinity. These expansions show that…
A cylindrically symmetric perfect fluid spacetime with no curvature singularity is shown. The equation of state for the perfect fluid is that of a stiff fluid. The metric is diagonal and non-separable in comoving coordinates for the fluid.…
Based on Eddington affine variational principle on a locally product manifold, we derive the separate Einstein space described by its Ricci tensor. The derived field equations split into two field equations of motion that describe two…
We consider the 3-dimensional formulation of Einstein's theory for spacetimes possessing a non-null Killing field $\xi^a$. It is known that for the vacuum case some of the basic field equations are deducible from the others. It will be…
In this paper, we consider the Cauchy problem for pressureless gases in two space dimensions with generic smooth initial data (density and velocity). These equations give rise to singular curves, where the mass has positive density…
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…
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 study the singularity formation of smooth solutions of the relativistic Euler equations in $(3+1)$-dimensional spacetime for both finite initial energy and infinite initial energy. For the finite initial energy case, we prove that any…
The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the ``first'' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classes of…
A numerical solution of Einstein field equations for a spherical symmetric and stationary system of identical and auto-gravitating particles in phase transition is presented. The fluid possess a perfect fluid energy momentum tensor, and the…
In Special Relativity, massless objects are characterized as either vacuum states or as radiation propagating at the speed of light. This distinction extends to General Relativity for asymptotically flat initial data sets (IDS) \((M^n, g,…
Spherically symmetric static fluid sources are endowed with rotation and embedded in Kerr empty space-time up to an including quadratic terms in an angular velocity parameter using Darmois junction conditions. Einstein's equation's for the…
The space of the solutions of the differential equations resulting from considering matter fluids of scalar field type or perfect fluid in Einstein-aether theory is analyzed. The Einstein-aether theory of gravity consists of General…
The thermodynamic behaviour of a relativistic perfect simple fluid obeying the equation of state $p=(\gamma-1)\rho $, where $0 \le \gamma \le 2$ is a constant, has been investigated. Particular cases include: vacuum($p=-\rho $, $\gamma=0$),…
In a recent series of papers new exact analytical solutions of the Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of different kinds of fluids have been displayed, [Phys. Rev. D {\bf…
This work is concerned with the finiteness problem for static, spherically symmetric perfect fluids in both Newtonian Gravity and General Relativity. We derive criteria on the barotropic equation of state guaranteeing that the corresponding…
The aim of this paper is to study geometrical aspects of static spacetime admitting an almost gradient Ricci soliton. Among others, We first determine the conditions under which the base manifold of static spacetime possess an almost…
Spatially homogeneous but totally anisotropic and non-flat Bianchi type II cosmological model has been studied in general relativity in the presence of two minimally interacting fluids; a perfect fluid as the matter fluid and a hypothetical…
These lectures are designed to provide a general introduction to the Einstein-Vlasov system and to the global Cauchy problem for these equations. To start with some general facts are collected and a local existence theorem for the Cauchy…