Testing strong-field gravity with tidal Love numbers

TL;DR

This paper investigates the tidal Love numbers of various compact objects, including black holes and exotic alternatives, to test the nature of these objects and the underlying theories of gravity using current and future gravitational-wave detectors.

Contribution

It extends the calculation of TLNs to exotic objects and alternative gravity theories, and evaluates the potential of gravitational-wave detectors to measure these effects.

Findings

Black holes have vanishing TLNs in classical GR.

Exotic objects show non-zero TLNs with universal features.

Future detectors can constrain or detect TLNs, testing gravity theories.

Abstract

The tidal Love numbers (TLNs) encode the deformability of a self-gravitating object immersed in a tidal environment and depend significantly both on the object's internal structure and on the dynamics of the gravitational field. An intriguing result in classical general relativity is the vanishing of the TLNs of black holes. We extend this result in three ways, aiming at testing the nature of compact objects: (i) we compute the TLNs of exotic compact objects, including different families of boson stars, gravastars, wormholes, and other toy models for quantum corrections at the horizon scale. In the black-hole limit, we find a universal logarithmic dependence of the TLNs on the location of the surface; (ii) we compute the TLNs of black holes beyond vacuum general relativity, including Einstein-Maxwell, Brans-Dicke and Chern-Simons gravity; (iii) We assess the ability of present and future gravitational-wave detectors to measure the TLNs of these objects, including the first analysis of TLNs with LISA. Both LIGO, ET and LISA can impose interesting constraints on boson stars, while LISA is able to probe even extremely compact objects. We argue that the TLNs provide a smoking gun of new physics at the horizon scale, and that future gravitational-wave measurements of the TLNs in a binary inspiral provide a novel way to test black holes and general relativity in the strong-field regime.