Higher derivative gravity black holes and the attractor mechanism in higher dimensions

Abstract

This Ph.D. thesis is made of two major parts, the investigation of black hole solutions in higher derivative gravity and the generalization of the attractor mechanism to hot black holes in arbitrary dimensions. The investigation of black hole solutions in higher derivative gravity was inspired by the possibility that the Schwarzschild black hole may not be the unique spherically symmetric vacuum solution to generalizations of general relativity. We consider black holes in pure fourth order higher derivative gravity treated as an effective theory where the Lagrangian is truncated to terms which are second order powers of the curvature. These higher order terms are of interest to us because they arise in effective descriptions of gravity and proposed theories of quantum gravity like string theory [1]. The solutions of this theory are called non-Schwarzschild black hole solutions, and they have been studied before [1] but we have put earlier results on a firmer footing by finding a systematic asymptotic expansion for the black holes and matching them with known numerical solutions obtained by integrating out from the near horizon region. Such solutions may be of interest in addressing the issue of higher derivative hair or during the later stages of black hole evaporation. These asymptotic expansions can be cast in the form of trans-series expansions which we conjecture will be a generic feature of non-Schwarzschild higher derivative black holes. Although we find a new branch of solutions, as found in earlier work [1], solutions only seem to exist for black holes with large curvatures meaning that one should not generically neglect even higher derivative corrections. This suggests that one effectively recovers the no-hair theorems in this context. We also study these black hole solutions by looking at their structure, and their properties such as their mass, temperature, and entropy. In the second part of the thesis, we extend the previous work of [2] on hot black hole attractors, by considering higher dimensions and the presence of a scalar potential (which is relevant for asymptotically AdS spaces and gauged supergravity). While, earlier work [2, 3] showed that the product of horizon areas is the geometric mean of the extremal area – we find that in the presence of a scalar potential this property no longer holds. When one complexifies the radial coordinate the non-extremal black hole solutions result in other horizons in addition to the classical event horizon of a black hole and the Cauchy horizons. In this work, we generalize the attractor mechanism for extremal black holes by proving that the product of all black hole horizon areas is independent of variations of the asymptotic moduli [4]. By adding the scalar potential we find that the product of horizon areas is not the geometric mean of the extremal area, which typically is true in gauged supergravity. Finally, we sketch the derivation of horizon invariants for stationary backgrounds