Accelerating a Black Hole in Higher Dimensions

TL;DR

This paper develops perturbative solutions for accelerating black holes in higher dimensions using the master equation with source, revealing limitations in constructing localized braneworld black holes in dimensions greater than four.

Contribution

It introduces a method to construct perturbative solutions for accelerated black holes in higher dimensions and analyzes their implications for braneworld black hole configurations.

Findings

Solutions are uniquely determined by local string tension.

Constant tension strings do not allow brane configurations in dimensions > 4.

Infinite localized solutions exist in 4D with non-uniform tension.

Abstract

Utilising the master equation with source for perturbations of the Schwarzschild-Tangherlini solution, we construct perturbative solutions representing a black hole accelerated by a string in higher dimensions. We show that such solutions can be uniquely determined by a single function representing the local tension of the string, under natural asymptotic and regularity conditions. We further study whether we can construct a localised braneworld black hole solution from such a solution by cutting off a region containing the string by a hypersurface and putting a vacuum brane on the boundary. We find that the solution corresponding to the string with constant tension does not allow such brane configuration when the bulk spacetime dimension is greater than four, in contrast to the four dimensional case. Further, we show that there exist infinitely many localised braneworld black hole solutions in the perturbative sense for four-dimensional bulk spacetime, if we allow non-uniform string tensions.