Black Holes in Higher Dimensional General Relativity

TL;DR

This paper reviews higher-dimensional black holes in General Relativity, focusing on how extended objects and ultra-spinning dynamics lead to non-spherical topologies, highlighting the complex landscape of higher-dimensional black hole solutions.

Contribution

It provides a detailed review and analysis of higher-dimensional black holes, emphasizing the role of extended objects and ultra-spinning rotations in creating diverse topologies.

Findings

Extended black objects exhibit non-spherical topologies.

Ultra-spinning black holes lead to unique horizon geometries.

Higher-dimensional gravity shows richer solution structures.

Abstract

This work is originally a Cambridge Part III essay. Throughout the paper, some aspects of General Relativity in higher dimensions are reviewed. The work presented draws a path within the wide landscape of higher dimensional black holes theory towards a specific objective: understanding how the combination of extended black objects and ultra-spinning rotation dynamics give rise to black hole topologies that depart from sphericity. The discussion aims to offer a compromise between giving a reasonably wide picture of the area of higher dimensional black holes, while at the same time going into detailed calculations that make manifest the enhanced nature of General Relativity in $d>4$.