Quasinormal ringing on the brane

While the linear behavior of gravity in braneworld models is well understood, much less is known about full non-linear gravitational effects. Even when they agree at the linear level, these could be expected to distinguish braneworlds from a lower-dimensional theory with no brane. Black holes are a good testing ground for such studies, as they are nonlinear solutions that would be expected to reflect the background geometry. In particular, we assess the role of black hole quasinormal modes in gravitational experiments devised to be sensitive to the existence of the brane, in a lower-dimensional setting where we have analytical control. We compute quasinormal modes of brane-localized black holes and find that they follow the entropy of the corresponding black hole. This observation allows us to conclude that, surprisingly, the scattering problem we consider, at least in some regimes, does not distinguish between non-linear gravitational effects of black holes in AdS space with a brane and black holes in a spacetime of one lower dimension.
Comment: 21 pages, 5 figures; v2: A few clarifications and table added. Version published in Class. Quant. Grav. 33 (2016) no.24, 245013