Geometry of higher dimensional black holes

TL;DR

This paper explores higher-dimensional vacuum solutions in Einstein's theory, analyzing specific metrics like Tangherlini and Myers-Perry, and examining their symmetries, causal structures, and continuations.

Contribution

It generalizes symmetry definitions and provides detailed analysis of higher-dimensional black hole solutions, including their causal and geometric properties.

Findings

Derived Kruskal extension of Tangherlini metric

Analyzed causal structure of Myers-Perry black holes

Discussed symmetry generalizations in higher dimensions

Abstract

This article investigates higher dimensional vacuum solutions of the Einstein equations. Generalizations of the definitions of spherical and axial symmetry to higher dimensions are discussed before analyzing specific solutions bearing one of these symmetries. The effective motions of the Tangherlini metric are calculated and its Kruskal continuation is derived. Also the Myers-Perry metric is analyzed with respect to its causal and horizontal structure.