Black holes, vacuum decay and thermodynamics

In this thesis we study two fairly different aspects of gravity: vacuum decay seeded by black holes and black hole thermodynamics. The first part of this work is devoted to the study of black holes within the (higher dimensional) Randall- Sundrum braneworld scenario and their effect on vacuum decay rates. We argue that, in close parallel to the 4-dimensional case, the decay rate is given by the difference in areas between the seeding and remnant black holes. We follow a brane approach to study the effective equations on the brane and focus on the tidal solution given by Dadhich et al. We solve numerically the equations of motion of a Higgs- like scalar field and obtain its decay rate. We then compare it to the Hawking evaporation rate and find that black holes of certain masses are likely to trigger vacuum decay. Finally, we study decay in the absence of a black hole and determine that, in close analogy to the 4-dimensional case, it is the presence of the black hole that enhances vacuum decay rates. The second part of this thesis discusses the thermodynamics of charged, rotating, accelerating AdS black holes. We impose sensible physical restrictions to the black hole metric and translate them into bounds of the black hole parameter space. We discuss the implications of having an exothermic term in the definition of enthalpy. We then focus on critical black holes, i.e. spacetimes in which at least one of the sides of the black hole’s rotation axis has a conical deficit of 2π. Finally, we consider the Penrose process for neutrally charged critical black holes and discuss about the definition of efficiency in this process.