Windows on Quantum Gravity

Abstract

These are notes for a graduate course in quantum gravity planned at IFT‐UAM/CSIC for the spring term of 2020, but delayed for an indefinite period of time (although a shortened version was given in the Escuela de Física (Institute of Physics) in the University of Costa Rica.). The aim of the course was to highlight the most important conceptual problems in the field and to summarize some of the most imaginative solutions to them that have been proposed in the literature. The course can best be characterized as idiosyncratic rather than encyclopedic.

Covariant techniques in Quantum Field Theory

“…Quadratic theories of gravity are renormalizable as opposed to General Relativity (cf. [55] for a general review of quantum gravity and some approaches to the problem), so the study of this kind of theories in the first order formalism could give rise to a unitary and renormalizable theory of gravity [56,57]. In this context, the computation to one-loop order for the linear Einstein-Hilbert action paves the way for future studies of more complex theories.…”

Null Geodesics, Raychaudhuri Equation, Trapped Surfaces, and Penrose Singularity Theorem

“…It is important to emphasize the well-known fact that all the "classical" singularity theorems, P.S.T., as well as the theorems in [10] and [11], are purely classical in the technical sense i.e. they exclude any reference to quantum mechanics, obviously due to the still missing complete theory of quantum gravity [12]. Some attempt to see a modification of the classical predictions with, however, opposite conclusions are, e.g., those in [13] and [14].…”

“…′′ ). The quotation marks in "quantum" is due to the still missing existence of a final theory of quantum gravity ([12]). As a concrete example ([16]), we consider the evolution of the ingoing radial null geodesic congruences within the black hole (B.H.)…”

Structural stability of spherical horizons

“…We would like to stress the fact that this is an issue independently of whether the ultraviolet (UV) completion of general relativity is to be based upon new (even non-geometric) variables, such as strings (cf. [15] and references therein).…”