Black Holes in Supergravity with Applications to String Theory

TL;DR

This thesis explores black hole solutions in four-dimensional ungauged Supergravity, revealing new classes of quantum black holes, their symmetries, and applications to string theory, including non-perturbative effects and dual conformal field theories.

Contribution

It characterizes general black hole solutions, introduces the H-F.G.K. formalism for non-supersymmetric solutions, and constructs quantum black holes with quantum corrections in string theory contexts.

Findings

Derived full Virasoro algebra for Supergravity black holes

Constructed all supersymmetric black-hole metrics in extended Supergravities

Obtained quantum black holes with quantum corrections in Type-IIA string compactifications

Abstract

This thesis is devoted to the study of black hole solutions in ungauged four-dimensional extended Supergravity. We characterize the most general spherically symmetric and static black-hole solution of ungauged Supergravity, and use the result to study the hidden conformal symmetries of Supergravity black holes, obtaining the full Virasoro algebra of the dual conformal field theory. We obtain also all the supersymmetric black-hole metrics of all extended Supergravities using the properties of the groups of Type E7. We introduce the H-F.G.K. formalism, which simplifies the construction of non-supersymmetric black-hole solutions in N=2 Supergravity, and apply it to a class of theories corresponding to Type-IIA String Theory compactified on a Calabi-Yau threefold. As a result we obtain the so-called "quantum" black holes, which only exist when certain quantum corrections (perturbative or non-perturbative, depending on the solution) are included in the prepotential. For the case of non-perturbative black holes, we elaborate on the potential consequences of the appearance on the solution of multi-valued functions in relation to the no-hair theorem for four-dimensional black holes. This thesis also contains the relevant mathematical background to formulate extended ungauged Supergravity in four-dimensions, that is, Special K\"ahler Geometry and homogeneous spaces, as well as a brief introduction to the mathematical structure of four-dimensional extended ungauged Supergravity.