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We study stationary axially symmetric solutions of the Einstein vacuum field equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. We…
We investigate the physical properties of equilibrium sequences of non-self-gravitating surfaces that characterize thick disks around a rotating deformed compact object described by a stationary generalization of the static q-metric. The…
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a…
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…
A new exact static interior solution of the Einstein equations is obtained for a gravitating ball filled with a Pascal perfect fluid . The solution is an extension of the well-known interior solution with a parabolic distribution of mass…
The FHP algorithm allows to obtain the relativistic multipole moments of a vacuum stationary axisymmetric solution in terms of coefficients which appear in the expansion of its Ernst's potential on the symmetry axis. First of all, we will…
The exact axisymmetric and static solution of the Einstein equations coupled to axisymmetric and static gravitating scalar (or phantom) field is presented. The spacetimes modified by the scalar field are explicitly given for the so called…
Locally rotationally symmetric perfect fluid solutions of Einstein's gravitational equations are matched along the hypersurface of vanishing pressure with the NUT metric. These rigidly rotating fluids are interpreted as sources for the…
The scope of this talk is to present some preliminary results on an effort, currently in progress, to generate an exact solution of Einstein's equation, suitable for describing spacetime around a rotating compact object. Specifically, the…
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…
It is known that B\"acklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior…
A, recently presented, general procedure to find static and axially symmetric, interior solutions to the Einstein equations, is extended to the stationary case, and applied to find an interior solution for the Kerr metric. The solution,…
We use the model approach to the description of spherical gravitating static fluid ball with an electric charge in general relativity. The metric is written in Bondi's coordinates. The total energy-momentum tensor (EMT) is chosen as a sum…
When solving the equations of General Relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress-energy. This implies that for static and isotropic spacetimes, the most general natural…
We reduce Einstein's field equations for the interior of a uniformly rotating, axisymmetric perfect fluid to a system of six second order partial differential equations for the pressure p the energy density $\mu$ and four dependent…
The Hartle-Thorne metric is an exact solution of vacuum Einstein field equations that describes the exterior of any slowly and rigidly rotating, stationary and axially symmetric body. The metric is given with accuracy up to the second order…
In this paper we use the second order formalism of Hartle to study slowly and rigidly rotating stars with focus on the quadrupole moment of the object. The second order field equations for the interior fluid are solved numerically for…
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear…
In an important series of articles published during the 70's, Krasi\'nski displayed a class of interior solutions of the Einstein field equations sourced by a stationary isentropic rotating cylinder of perfect fluid. However, these…