Tidal Love Numbers of Braneworld Black Holes and Wormholes

TL;DR

This paper investigates the tidal Love numbers of black holes and wormholes within the Randall-Sundrum braneworld model, revealing that quadrupolar Love numbers are generally non-zero and could serve as signatures of extra-dimensional effects in gravitational wave signals.

Contribution

It provides a detailed analysis of tidal deformations and Love numbers for braneworld black holes and wormholes, highlighting their potential as observational signatures of extra dimensions.

Findings

Quadrupolar Love numbers are generally non-zero.

Tidal deformation equations reduce to specific ODEs.

Potential gravitational wave signatures of braneworld effects.

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 ODE or a homogeneous third-order ODE of 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 that in particular the quadrupolar TLN is generically non-vanishing. Thus it could be a signature of a braneworld by virtue of its potential appearance in gravitational waveforms emitted in binary merger events.