Gravitational collapse and entropy of Black Holes with magnetic sources

TL;DR

This thesis explores the effects of magnetic sources on gravitational collapse and black hole entropy, revealing anisotropic collapse behaviors and deviations from the Bekenstein-Hawking area law in higher dimensions.

Contribution

It provides numerical solutions for magnetized, self-gravitating fermion gases in anisotropic spacetimes and calculates black hole entropy with higher-order corrections, extending previous models.

Findings

Neutron gas collapse is isotropic, electron gas collapse is anisotropic due to magnetic coupling.

Black hole entropy deviates from the Bekenstein-Hawking law when higher-order Riemann invariants are included.

Collapse behavior depends on the type of fermionic matter and magnetic interactions.

Abstract

This thesis is divided in two parts, each one addressing problems that can be relevant in the study of compact objects. The first part deals with the study of a magnetized and self-gravitating gas of degenerated fermions (electrons and neutrons) as sources of a Bianchi-I space-time. We solve numerically the Einstein-Maxwell field equations for a large set of initial conditions of the dynamical variables. The collapsing singularity is isotropic for the neutron gas and can be anisotropic for the electron gas. This result is consistent with the fact that electrons exhibit a stronger coupling with the magnetic field, which is the source of anisotropy in the dynamical variables. In the second part we calculate the entropy of extremal black holes in 4 and 5 dimensions, using the entropy function formalism of Sen and taking into account higher order derivative terms that come from the complete set of Riemann invariants. The resulting entropies show the deviations from the well know Bekenstein-Hawking area law.