Autogravitação para espaços-tempos estáticos e isotrópicos com aplicações a modelos de interesse astrofísico

Abstract

In this work I consider the equations of self-gravitation for collisionless, static and isotropic systems in the context of the theory of general relativity. From these I present the form of the distribution function when we consider two equations of state, and demonstrate the impossibility of self-consistent models with equations of state of the form P^T = kP^r and P^r = \omega \rho, when k is a half integer. As an application of interest in astrophysics, I intend to extend the Newtonian models belonging to the Hypervirial family to general relativity, focusing on the Hernquist model. For this I use a solution analogous to static perfect fluid solutions with spherical symmetry, which, through the equations of self-gravitation, allows obtaining a distribution function consistent with the aforementioned metric. I present how to establish a limit for the mass of the system using this distribution function.