Black holes, vacuum decay and thermodynamics

Abstract

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.