On the Localisation of 4-Dimensional Brane-World Black Holes

In the context of brane-world models, we pursue the question of the existence of 5-dimensional solutions describing regular black holes localised close to the brane. Employing a perturbed Vaidya-type line-element embedded in a warped fifth dimension, we attempt to localise the extended black-string singularity, and to restore the regularity of the AdS spacetime at a finite distance from the brane by introducing an appropriate bulk energy-momentum tensor. As a source for this bulk matter, we are considering a variety of non-ordinary field-theory models of scalar fields either minimally-coupled to gravity, but including non-canonical kinetic terms, mixing terms, derivative interactions and ghosts, or non-minimally-coupled to gravity through a general coupling to the Ricci scalar. In all models considered, even in the ones characterised by a high-degree of flexibility, a negative result was reached. Our analysis demonstrates how difficult the analytic construction of a localised brane-world black hole may be in the context of a well-defined field-theory model. Finally, with regard to the question of the existence or not of a static classical black hole solution on the brane, our analysis suggests that such solutions could in principle exist, however, the associated field configuration itself has to be dynamic.