Lovelock gravity, black holes and holography

Abstract

Lovelock theory is the natural extension of General Relativity to higher di- mensions and can also be thought of as a toy model for ghost-free higher curvature gravity. These gravity theories capture some of the de ning fea- tures of higher curvature gravities, namely the existence of more than one (A)dS vacuum and an intricate dynamics, more general black hole solutions and instabilities; while avoiding some of their problems. In particular, Love- lock gravities yield second order eld equations so that they can be considered beyond the perturbative regime and are free of higher derivative ghosts. This provides an appealing arena to explore di erent gravitational and holographic aspects of higher curvature gravity. Most of the vacua of the theory support black holes that display inter- esting features. Besides, black holes with maximally symmetric horizons are subject to a version of Birkho 's theorem and their solutions can be found analytically. Most e orts in the literature have been devoted however to one particular branch of solutions, often restricted to a speci c combination of the Lovelock couplings. The branch usually chosen for the analysis is the so- called EH-branch, as it actually reduces to the general relativistic solution as we turn o the higher order couplings. In this thesis we have presented some tools that allow for the description of Lovelock black holes for arbitrary values of the whole set of couplings, dimensionality and order of the theory. Despite the fact of the solution being implicit, it is possible to extract most relevant information and discuss all possible cases in the general situation, analyze the number of horizons, the thermodynamic stability of the solution, phase transitions, etc. Furthermore, this approach has been generalized to the case of charged and cosmological solutions, and also to the so called quasi-topological gravities, that share the same functional form of the black hole solutions with the Lovelock family while being lower dimensional. Our method is very useful to gain intuition about physical processes in- volving black holes. One can easily visualize the evolution of the position and number of horizons as the mass of the solution varies, this providing crucial information about, for instance, the possible appearance of naked singulari- ties or the violation of the third law of thermodynamics. We have seen that the rigid symmetry imposed on the solution naively allows such problematic behavior which is avoided once the stability of the solution is taken into full consideration.