Distorted 5-dimensional vacuum black hole
arXiv:1009.5971 · doi:10.1103/PhysRevD.82.124039
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.
20 pages, 9 figures
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