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Autogravitação para espaços-tempos estáticos e isotrópicos com aplicações a modelos de interesse astrofísico
(Universidade Federal de São Carlos, 2012-11-24) Gauy, Henrique Matheus; Ramos-Caro, Javier Fernando; https://lattes.cnpq.br/2067343302764973; https://lattes.cnpq.br/1412367289023716
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.