Distorted 5-dimensional vacuum black hole

TL;DR

This paper investigates how external matter distortion affects 5-dimensional Schwarzschild-Tangherlini black holes, revealing dualities, topological similarities near singularities, and how distortions influence the black hole's internal structure and horizon properties.

Contribution

It introduces a class of distorted 5D black hole solutions with specific symmetries and explores their duality relations, topology, and effects on singularity proximity and horizon characteristics.

Findings

Existence of a duality between horizon and singularity surfaces.

Distortions can bring the singularity closer to the horizon.

The topology near the singularity remains similar to the undistorted case.

Abstract

In this paper we study how the distortion generated by a static and neutral distribution of external matter affects a 5-dimensional Schwarzschild-Tangherlini black hole. A solution representing a particular class of such distorted black holes admits an RxU(1)xU(1) isometry group. We show that there exists a certain duality transformation between the black hole horizon and a stretched singularity surfaces. The space-time near the distorted black hole singularity has the same topology and Kasner exponents as those of a 5-dimensional Schwarzschild-Tangherlini black hole. We calculate the maximal proper time of free fall of a test particle from the distorted black hole horizon to its singularity and find that, depending on the distortion, it can be less, equal to, or greater than that of a Schwarzschild-Tangherlini black hole of the same horizon area. This implies that due to the distortion, the singularity of a Schwarzschild-Tangherlini black hole can come close to its horizon. A relation between the Kretschmann scalar calculated on the horizon of a 5-dimensional static, asymmetric, distorted black hole and the trace of the square of the Ricci tensor of the horizon surface is derived.