Black Holes in a Compactified Spacetime

TL;DR

This paper analyzes the properties of Schwarzschild black holes in a spacetime with one compactified dimension, revealing horizon distortion, deriving an analytical approximation, and discussing potential instabilities.

Contribution

It provides a new analytical approach to describe distorted black holes in compactified spacetimes, extending previous solutions and exploring stability issues.

Findings

Derived an analytical approximation for the distorted horizon

Identified horizon shape and surface gravity changes due to compactification

Discussed potential instabilities of black holes in compactified spaces

Abstract

We discuss properties of a 4-dimensional Schwarzschild black hole in a spacetime where one of the spatial dimensions is compactified. As a result of the compactification the event horizon of the black hole is distorted. We use Weyl coordinates to obtain the solution describing such a distorted black hole. This solution is a special case of the Israel-Khan metric. We study the properties of the compactified Schwarzschild black hole, and develop an approximation which allows one to find the size, shape, surface gravity and other characteristics of the distorted horizon with a very high accuracy in a simple analytical form. We also discuss possible instabilities of a black hole in the compactified space.