Topological Black Holes -- Outside Looking In

TL;DR

This paper explores the mathematical construction and physical properties of topological black holes with non-trivial horizon topologies across multiple dimensions, including their interior structures and scalar field behavior.

Contribution

It provides a unified framework for topological black holes in various dimensions and analyzes scalar field decay, highlighting differences from spherical cases.

Findings

Distinct radiative decay patterns for scalar fields in topological black holes.

Comprehensive construction covering all known special cases.

Insights into interior structures of massive charged topological black holes.

Abstract

I describe the general mathematical construction and physical picture of topological black holes, which are black holes whose event horizons are surfaces of non-trivial topology. The construction is carried out in an arbitrary number of dimensions, and includes all known special cases which have appeared before in the literature. I describe the basic features of massive charged topological black holes in $(3+1)$ dimensions, from both an exterior and interior point of view. To investigate their interiors, it is necessary to understand the radiative falloff behaviour of a given massless field at late times in the background of a topological black hole. I describe the results of a numerical investigation of such behaviour for a conformally coupled scalar field. Significant differences emerge between spherical and higher genus topologies.