New approaches to higher-dimensional general relativity

TL;DR

This thesis explores advanced mathematical frameworks for classifying and analyzing higher-dimensional spacetimes in general relativity, with applications to black hole stability.

Contribution

It introduces new algebraic classification methods, extends the Goldberg-Sachs theorem to higher dimensions, and applies these to black hole stability analysis.

Findings

Development of higher-dimensional Geroch-Held-Penrose formalism

Partial generalization of Goldberg-Sachs theorem

Insights into extremal black hole stability

Abstract

This PhD thesis contains a collection of work related to the algebraic classification of spacetimes in higher dimensions, including an up-to-date review of various aspects of the field. The work discussed includes the higher-dimensional Geroch-Held-Penrose formalism, a partial generalization of the Goldberg-Sachs theorem to higher-dimensions, and applications of these results to studying the stability of extremal black holes.