Physics and Geometry of Gravity at High Energies

In this thesis defense we study physical and geometric aspects of gravity at high energies. On the one hand, we carry out a detailed investigation of gravitational physics in this regime with the aid of higher-order gravities. These are extensions of General Relativity including terms in higher derivatives of the metric and other fields which, in addition to an effective field theory interpretation, possess as well an intrinsic interest by themselves. More concretely, we focus on higher-order gravities of the (Generalized) Quasitopological class, defined as those admitting static and spherically symmetric solutions characterized by a single function satisfying an equation of, at most, second order. We consider the addition of a U(1) gauge vector field and identify infinite families of Electromagnetic (Generalized) Quasitopological Gravities (E(G)QGs). We establish several intriguing properties of these theories and explore their charged, static and spherically symmetric solutions. In particular, we prove that a subset of EQGs allows for completely regular electrically-charged black holes for arbitrary mass and non-vanishing charge. 

On the other hand, we study geometric properties of gravity at high energies. In particular, we explore real parallel spinors on globally hyperbolic four-manifolds. We are able to reformulate the problem in terms of a system of differential equations for a family of functions and coframes on a Cauchy surface that we call the parallel spinor flow. Remarkably, we find that the parallel spinor and the Einstein flows coincide on common initial data, thus providing an initial data characterization of a real parallel spinor on a Ricci flat globally hyperbolic four-manifold. 

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Ángel J. Murcia Gil

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'Physics and Geometry of Gravity at High Energies'