Exploring the extreme effects ofrotation and electromagnetic fields in general relativity: new exact solutions and numerical approximations

Abstract

This research project aims to investigate compact rotating objects taking into account electromagnetic fields and other sources that model the different forms of matter and energy that can be useful in the context of astrophysics and cosmology. In the language of General Relativty (GR), this consists in studying compact objects such as black holes, black holes regular, quasi-black holes and stars that are described by stationary axi-symmetric spacetimes. The analysis will be done through the Einstein-Maxwell field equations, assuming that the matter that makes up the object is a perfect (or anisotropic) rotating fluid, with electric charge. The first objective of this project is to generalize, to the stationary case, well-known theorems in the literature, that arose from Weyl's hypothesis in assuming a functional relation between the metric potential and the electrical potential, which were recently compiled by Lemos and Zanchin [Phys. Rev. D 80, 024010 (2009)]. From these theorems, another objective is to analyze exact solutions that describe electrically charged compact objects in rotation, which can be obtained, for example, through the Newman-Janis algorithm and its modifications, in order to explore all types of objects that the Einstein-Maxwell field equations allows. Finally, a third important objective is the analysis of the stability of the new models and the possible comparison with observation data. (AU)