Related papers: A rotating three component perfect fluid source an…
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…
In this thesis four separate problems in general relativity are considered, divided into two separate themes: coordinate conditions and perfect fluid spheres. Regarding coordinate conditions we present a pedagogical discussion of how the…
Kerr-Schild solutions to the vacuum Einstein equations are considered from the viewpoint of integral equations. We show that, for a class of Kerr-Schild fields, the stress-energy tensor can be regarded as a total divergence in Minkowski…
We present a novel approach for the construction of interior solutions for the Kerr metric, extending J. Ovalle's foundational work through ellipsoidal coordinate transformations. By deriving a physically plausible interior solution that…
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…
We present the Ernst potential and the line element of an exact solution of Einstein's vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass…
We construct a new rotating solution of Einstein's theory in vacuum by exploiting the Lie point symmetries of the field equations in the complex potential formalism of Ernst. In particular, we perform a discrete symmetry transformation,…
We obtain a new class of rotating black holes for Einstein theory with perfect fluid source in (2+1) dimensions. We conclude that these black hole solutions only depend on variable angular velocity $m(r)$. Some examples of these black holes…
We present a family of exact rotating anisotropic fluid solutions, which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor $R_{\mu\nu}$ the eigenvalues of the tensor $R_\mu^\nu$ and the…
While non-rotating black-hole solutions are well known in Einstein--\ae{}ther gravity, no axisymmetric solutions endowed with Killing horizons have been so far found outside of the slowly rotating limit. Here we show that the Kerr spacetime…
We consider a self-gravitating, rigidly rotating charged perfect fluid immersed in the Wald magnetosphere, constructed out of two linearly independent Killing vectors present in stationary and axially-symmetric spacetimes. We show that in…
A class of stationary rigidly rotating perfect fluid coupled with non-linear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found, for the equation of state…
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
We study spherically symmetric geometries made of anisotropic perfect fluid based on general relativity. The purpose of the work is to find and classify black hole solutions in closed spacetime. In a general setting, we find that a static…
In a recent series of papers new exact analytical interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. A fluid with an axially directed pressure has been first considered, then a perfect fluid,…
The Kerr metric is a vacuum solution of the Einstein equations outside of a rotating black hole, but what interior matter is actually rotating and sourcing the Kerr geometry? Here, we describe a rotating exotic matter which can source the…
We determine the energy-momentum tensor of non-perfect fluids in thermodynamic equilibrium. To this end, we derive the constitutive equations for energy density, isotropic and anisotropic pressure as well as for heat-flux from the…
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…
Charged static and rotating objects as solutions of the Einstein-Maxwell field equations are obtained and studied in the present work. The full spacetime geometry is obtained by matching two spacetime regions, an interior region containing…
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…