Black holes and the generalized second law of thermodynamics

Abstract

In the last decades, research in black hole physics has shown a deep relation between black holes, thermodynamics, and quantum mechanics. In a semiclassical context, black holes are not black, they have a {\em temperature} $T_{\rm H}\equiv \kappa/2\pi$ and an {\em entropy} $S_{\rm BH}\equiv A_{\rm BH}/4$ proportional to its surface gravity $\kappa$ and area $A_{\rm BH}$ respectively. This striking connection is reinforced when one analyzes the so called {\em generalized second law}, which states that the total entropy of matter outside the black hole plus the entropy of the black hole never decrease. In this master's project, we intend to investigate the generalized second law on two complementary fronts. Firstly, due to its central role in interpreting black holes as thermodynamical entities, we will study general proofs of its validity. Secondly, we will analyze how one can use the generalized second law to extend the singularity theorems to the semi classical realm. (AU)