Tidal Love numbers of braneworld black holes and wormholes

Abstract

We study the tidal deformations of various known black hole and wormhole solutions in a simple context of warped compactification-Randall-Sundrum theory-in which the four-dimensional spacetime geometry is that of a brane embedded in five-dimensional anti-de Sitter spacetime. The linearized gravitational perturbation theory generically reduces to either an inhomogeneous second-order ordinary differential equation (ODE) or a homogeneous third-order ODE for which indicial roots associated with an expansion about asymptotic infinity can be related to tidal Love numbers. We describe various tidal-deformed metrics, classify their indicial roots, and find, in particular, that the quadrupolar tidal Love number is generically nonvanishing. Thus, it could be a signature of a braneworld by virtue of its potential appearance in gravitational waveforms emitted in binary merger events.