Lovelock gravity, black holes and holography

Abstract

In recent years, there has been a revival of interest in higher curvature theories of gravity. Higher order corrections to the Einstein-Hilbert action appear in any sensible theory of quantum gravity, either in the context of Wilsonian approaches, as next-to-leading orders in the effective action of String Theory or motivated by the possibility of higher dimensional spacetimes. In particular, Lovelock theories represent the most natural generalization of the Einstein-Hilbert action to dimensions larger than four. Moreover, its first non-trivial action, Lanczos-Gauss-Bonnet, also appears in "bona fide" realizations of String Theory, with the advantage that it can be considered as a finite correction. Gravity theories of the Lovelock type, yielding two derivative equations of motion, avoid some of the problems of other higher curvature gravities while capturing some of their characteristic features, namely the existence of several branches of solutions, more general solutions and complex dynamics. This class of theories provides a particularly suitable playground to test our ideas about gravity in a much broader context. We will investigate the consequences that follow from the assumption that the model is the classical limit of a fundamental theory, not an effective one. This attitude is also the most efficient one to eventually uncover reasons to reject the assumption. In the holographic context, the addition of higher curvature corrections allows for the description of more general field theories, e. g. CFTs with different central charges in four dimensions. Doing this in a controlled way, we will uncover previously unsuspected connections between some central concepts in physics, such as causality or positivity of the energy. These correlations extend smoothly and meaningfully to any dimension and any Lovelock theory, thus supporting the possibility that AdS/CFT may be applicable beyond the framework of String Theory, as long as there is a consistent theory of quantum gravity in AdS.