Relativistic Static Thin Disks of Polarized Matter

An infinite family of exact solutions of the electrovacuum Einstein-Maxwell equations is presented. The family is static, axially symmetric and describe thin disks composed by electrically polarized material in a conformastatic spacetime. The form of the conformastatic metric allows us to write down the metric functions and the electromagnetic potentials in terms of a solution of the Laplace equation. We find a general expression for the surface energy density of the disk, the pressure, the polarization vector, the electromagnetic fields and the velocity rotation for circular orbits. As an example, we present the first model of the family and show the behavior of the different physical variables.Comment: 7 pages, 4 figures, 70 and 70 Gravitation Fest, 28 September 2016, Cartagena, Colombi

Evolution of a mass-less test scalar field on Boson Stars space-times

We numerically solve the mass-less test scalar field equation on the space-time background of boson stars and black holes. In order to do so, we use a numerical domain that contains future null infinity. We achieve this construction using a scri-fixing conformal compactification technique based on hyperboloidal constant mean curvature foliations of the space-time and solve the conformally invariant wave equation. We present two results: the scalar field shows oscillations of the quasi- normal-mode type found for black holes only for boson star configurations that are compact, and no signs of tail decay is found in the parameter space we explored. Even though our results do not correspond to the master equation of perturbations of boson star solutions, they indicate that the parameter space of boson stars as black hole mimickers is restricted to compact configurations.Comment: 9 pages, 15 eps figures, revtex

Pseudo-Newtonian planar circular restricted 3-body problem

We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor-Hoenselaers-Perj\'es procedure, we perform an expansion in the mass potential of a static massive spherical source up to the first non-Newtonian term, giving place to a gravitational potential that includes first-order general relativistic effects. With this result, we model a system composed by two pseudo-Newtonian primaries describing circular orbits around their common center of mass, and a test particle orbiting the system in the equatorial plane. The dynamics of the new system of equations is studied in terms of the Poincar\'e section method and the Lyapunov exponents, where the introduction of a new parameter $\epsilon$, allows us to observe the transition from the Newtonian to the pseudo-Newtonian regime. We show that when the Jacobian constant is fixed, a chaotic orbit in the Newtonian regime can be either chaotic or regular in the pseudo-Newtonian approach. As a general result, we find that most of the pseudo-Newtonian configurations are less stable than their Newtonian equivalent.Comment: 11 pages, 2 figures. Accepted for publication in Physics Letters A, In Pres