Termodinâmica de buracos negros rodeados por diferentes fluidos, no contexto da Gravity’s Rainbow

Abstract

In this dissertation, we investigate the role of the introduction of a new observer-independent scale, the Planck scale, producing a modification in Theory of General Relativity (TGR) that became known as Gravity’s Rainbow (G’sR). We begin with a theoretical review of the fundamentals of Doubly Special Relativity (DSR), its extension to GsR, the modification of the structure of Einstein’s usual energy-moment dispersion relation, in which we consider the introduction of a new invariant, the Planck scale and the postulates of TGR. Later, we obtain the Schwarzschild and Kislev spacetime metrics, in the context of GsR, in which we observe that the metrics come to depend on the energy of the particles compared to the Planck energy. Then, a review of the thermodynamics of black holes in TGR is carried out in order to serve as a comparison of results between theories, together with an application to black holes surrounded by different cosmic fluids. Finally, in possession of the entire framework developed, we consider the thermodynamics of black holes in the context of G’sR, in which we study black holes immersed in different fluids and study how this space-time that depends on the energy of particles can influence the thermodynamic properties of black holes whose solutions were obtained in the framework og Gravity’s Rainbow