Black holes and self-gravitating structures: integrability, stability and chaos

Abstract

The central subject of this project is the model of black hole as an astrophysical object, i.e., a paradigm of compact object with a horizon. All the different aspects that we are interested have, in principle, an observational component. We shall study: a) the motion of test particles orbiting a black hole with different types of perturbations like, rings, disks, magnetic fields, bars, etc, and the motion around two black holes, in particular, the Hill problem and its possible relativistic and pseudo-relativistic extensions. This is a traditions subject of celestial mechanics wherein we add a general relativistic component; b) models of compact objects with structure (disks, rings, electric and magnetic fields, etc.). We search for exact solutions to the Einstein equation that can represent objects of astrophysical interest and that may be used in other applications like structure formation by central bodies in rotation, numerical simulations of swarm of particles and also test fluids. Study of linear stability of structures. We also search for integrable systems that can represent matter coupled or not to the Einstein equations. Solutions to the Fokker-Planck equations for particle distributions in Newtonian disks and its possible generalizations for relativistic disks; c) structure formation at the comogonic and cosmological level, stochastic contributions for the growth of small perturbations in the expanding universe. Extensions of the Einstenian relativity, especially multidimensional theories and theories with torsion. The problem of dark matter and dark energy The study of cosmic strings and other topological defects, classical and quantun singularities, existence and stability of geodesics and closed time like curves. The methology is strongly based on the use of computers as a tool for numerical, as well as, algebraic computation. (AU)