Higher-Curvature Gravity, Black Holes and Holography

Zusammenfassung

Higher-curvature theories of gravity are extensions of General Relativity (GR) that arise in effective descriptions of quantum gravity theories, such as String Theory. While at low energies the behaviour of the gravitational field in higher-curvature gravities is almost indistinguishable from the one predicted by GR, the differences can be dramatic in extreme gravity scenarios, such as in the case of black holes (BHs). It is therefore an exciting task to study how black hole geometries are modified by higher-curvature corrections, with the hope that some problematic characteristics of BHs observed in GR could be improved, providing hints on the effects of an underlying UV-complete theory of gravity. However, there are some difficulties associated with higher-derivative theories, such as the existence of instabilities, propagation of ghost modes, or simply the extreme complexity of the differential equations governing the dynamics of the gravitational field. In this thesis we identify a new family of higher-curvature gravities that avoid some of these problems. Known as Generalized quasi-topological gravities (GQGs), such theories represent extensions of GR that are free of instabilities and ghosts at the linear level, and whose equations of motion for static, spherically symmetric spaces acquire a sufficiently simple form so as to allow for the non-perturbative study of black hole solutions. The simplest non-trivial member of this family in four dimensions — and also the first one to be discovered — is known as Einsteinian cubic gravity, and it will have a starring role in this thesis. Besides the intrinsic interesting properties of GQGs, we argue that they capture the most general higher-derivative correction to GR when field redefinitions are included into the game. Then, we use these theories to study the non-perturbative corrections to the Schwarzschild black hole in four dimensions and we focus our attention on the modified thermodynamic relations. The most impressive prediction of these theories is that the Hawking temperature of static, neutral black holes vanishes in the zero-mass limit instead of diverging — which is the answer predicted by GR. As a consequence, small black holes become thermodynamically stable and their evaporation process takes an infinite time. In addition, higher-curvature gravities find very rewarding applications in the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence, a duality that relates a classical theory of gravity in AdS space to a quantum field theory that lives in the boundary of AdS. In this context, holographic higher-curvature gravities are useful toy models that we can use, for instance, to extract general lessons about the dynamics of CFTs or to question the generality of the predictions of holographic Einstein gravity. In this thesis we explore the holographic applications of four-dimensional Einsteinian cubic gravity, which provides a toy model for a non-supersymmetric holographic CFT in three dimensions. In addition, we construct new Euclidean-AdS-Taub-NUT solutions, which are dual to conformal field theories placed on squashed spheres. Using these results, we derive a universal expression for the expansion of the free energy of three-dimensional CFTs on squashed spheres up to cubic order in the deformation parameter.