Termodinâmica do buraco negro regular.

Abstract

This dissertation focuses on the relationship between black holes and thermodynamics, highlighting the importance of understanding the physical properties of these astrophysical objects. We begin our study with a brief review of Einstein’s field equations, which provide solutions describing various astrophysical objects and the overall evolution of the Universe within the field of Cosmology. However, some of these solutions with spherical symmetry, when considered in a vacuum, become inapplicable at r = 0 due to the presence of singularities. In this context, James Bardeen was one of the first to propose adjustments to the metric to overcome this incompatibility, leading to the emergence of the so-called Regular Black Holes. In the section dedicated to regular black holes, we discuss solutions that avoid the central singularity typical of Schwarzschild black holes. These solutions exhibit a region of thermal stability, indicating fundamental differences in their thermodynamic properties. This section also presents the regular metrics, including the Nozari-Mehdpour metric and the Bardeen metric, where in both cases the mass M is replaced by a function of r in order to eliminate the central singularity present in singular black holes. From these new metrics, we derive new event horizons and new characteristic functions for each metric, allowing us to study their behavior. Next, we present the laws of black hole thermodynamics and draw a parallel with the laws of classical thermodynamics. We revisit the studies of Bekenstein from the 1970s, which introduced the idea that black holes possess entropy. This entropy is related to the loss of information about what lies inside the black hole, being accessible only to an external observer. The proposal that the entropy of a black hole is linked to the area of its event horizon, which never decreases, is a central point of this discussion. Finally, we analyze the behavior of the regular thermodynamic properties, such as temperature, entropy, and heat capacity, associated with the predicted black hole.