Grant number: 16/00905-1 Support type: Scholarships in Brazil - Master Effective date (Start): July 01, 2016 Effective date (End): February 28, 2018 Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields Principal researcher: Andre Gustavo Scagliusi Landulfo Grantee: Ian Bernardes Barcellos Home Institution: Centro de Ciências Naturais e Humanas (CCNH). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil Associated research grant: 13/09357-9 - Physics and geometry of spacetime, AP.TEM 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)