Related papers: Cylindrically Symmetric Relativistic Fluids: A Stu…
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…
This paper is the first in a sequence of three devoted to the formulation of a theory of self-gravitating anisotropic fluids in both Newtonian and relativistic gravity. In this first paper we set the stage, place our work in the context of…
The special conformal transformation (composed by inversion - translation - inversion) is used to generate a time dependent conformally flat spacetime. In order to be an exact solution of Einstein's equations, we need as a source a stress…
We present a brief review of exact solutions of cylindrical symmetric fields in General Relativity produced by different perfect fluid sources. These sources are assumed static, stationary, translating and collapsing. Properties of these…
We study a gravitating spherically symmetric nonrelativistic configuration consisting of a spinor fluid whose effective equation of state is derived from a consideration of a limiting system supported by a massive nonlinear spinor field.…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
We examine the structure scalars constructed from the orthogonal splitting of the Riemann tensor for the spacetime metric describing the interior of a charged matter configuration undergoing dissipative collapse in the framework of $f(R,T)$…
It is shown, for the self-consistent system of scalar, electro-magnetic and gravitational fields in general relativity, that the equations of motion admit a special kind of solutions with spherical or cylindrical symmetry. For these…
We study different dimensional fluids inspired by noncommutative geometry which admit conformal Killing vectors. The solutions of the Einstein field equations examined specifically for five different set of spacetime. We calculate the…
Foundations of the analysis of scaling in randomly stirred compressible fluid with the aid of stochastic differential equations are discussed in the example of perfect gas. The structure of the stress tensor with nonnegative shear and bulk…
We have studied the dynamics of a cylindrical column of anisotropic, charged fluid which is experiencing dissipation in the form of heat flow, free-streaming radiation, and shearing viscosity, undergoing gravitational collapse. We calculate…
We set up the construction of generic (d+2)-dimensional metrics corresponding to (d+1)-dimensional fluids, representing holographically the hydrodynamic regimes of the putative dual theories. We give general seed equilibrium metrics…
An algorithm presented by K. Lake to obtain all static spherically symmetric perfect fluid solutions was recently extended by L. Herrera to the interesting case of locally anisotropic fluids (principal stresses unequal). In this work we…
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…
In this paper we consider dissipative hydrodynamic equations for systems with continuous broken symmetries. We first present the case of superfluidity, in which the symmetry U(1) is broken and then generalize to the chiral symmetry $SU(2)_L…
The recently proposed definition of complexity for static and spherically symmetric self--gravitating systems [1], is extended to the fully dynamic situation. In this latter case we have to consider not only the complexity factor of the…
A class of spherically symmetric spacetimes invariantly defined by a zero flux condition is examined first from a purely geometrical point of view and then physically by way of Einstein's equations for a general fluid decomposition of the…
A general procedure to find static and axially symmetric, interior solutions to the Einstein equations is presented. All the so obtained solutions, verify the energy conditions for a wide range of values of the parameters, and match…
We review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema\^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant…
The properties of some locally rotationally symmetric (LRS) perfect fluid space-times are examined in order to demonstrate the usage of the description of geometries in terms of the Riemann tensor and a finite number of its covariant…