Buraco negro de Kerr e quintessência - Brito, Nicolas Carvalho de (2018)
The present work starts by presenting a concise derivation of the Einstein’s field equations. After, we focus our attention on the static and spherically symmetric exact solutions of the Einstein equations, expliciting the two more basic solutions, which are the Schwarzschild solution and the Reissner-Nordstrom solution. We finish this part by presenting the concept of quintessense and by deriving the solution with quintessence. In turn, we present an algorithm, due to Ezra T. Newman and Allen I. Janis, best known as Newman-Janis ‘trick’, which allows us to obtain the Kerr solution, which represents gravitational fields due to a rotating body, from some algebraic manipulation. Possessing the Kerr solution in the presense of quintessence, we analize some properties of the solution and try to show the influence of the quintessence on rotating black holes, which can be extracted from the Kerr Solution. There are a lot of works on rotating black holes and quintessence, but none of them present in a detailed manner the algebraic development, what is one of the reasons why finding the Kerr solution is só hard and uncertain, mainly because there is no agreement about the validity and basis of the Newman-Janis algorithm, that’s why the main goal of this work is presenting, when possible, in a detailed manner, the steps from the basic principles of the General Theory of Relativity to the solution that describes a rotating black hole and present the influence of quintessence on these objects.