Accelerating a Black Hole in Higher Dimensions

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.