Eur. Phys. J. C (2012) 72: 2258
https://doi.org/10.1140/epjc/s10052-012-2258-9

Regular Article - Theoretical Physics

Schwarzschild generalized black hole horizon and the embedding space

¹ Departamento de Física e Química, Universidade Estadual Paulista, Av. Dr. Ariberto Pereira da Cunha, 333, Guaratinguetá, SP, Brazil
² Centro de Matemática, Computação e Cognição, Universidade Federal do ABC 09210-170, Santo André, SP, Brazil

^* e-mail: roldao.rocha@ufabc.edu.br

Received: 9 August 2012
Revised: 23 November 2012
Published online: 18 December 2012

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.