Schwarzschild generalized black hole horizon and the embedding space

TL;DR

This paper investigates how the embedding space affects black hole horizons in braneworld scenarios, revealing conditions under which black strings collapse and singularities form away from the brane.

Contribution

It introduces a Taylor expansion method to analyze black hole metrics in extra dimensions and identifies conditions leading to black string collapse and singularities.

Findings

Black hole horizon influenced by extra-dimensional embedding.

Existence of a Kottler correction related to black string collapse.

Singularity occurs when the black string radius approaches zero away from the brane.

Abstract

By performing a Taylor expansion along the extra dimension of a metric describing a black hole on a brane, we explore the influence of the embedding space on the black hole horizon. In particular, it is shown that the existence of a Kottler correction of the black hole on the brane, in a viable braneworld scenario, might represent the radius of the black string collapsing to zero, for some point(s) on the black string axis of symmetry along the extra dimension. Further scrutiny on such black hole corrections by braneworld effects is elicited, the well-known results in the literature are recovered as limiting cases, and we assert and show that when the radius of the black string transversal section is zero, as one moves away from the brane into the bulk, is indeed a singularity.