Tidal Love Numbers from EFT of Black Hole Perturbations with Timelike Scalar Profile

TL;DR

This paper uses effective field theory to analyze tidal Love numbers of black holes with scalar profiles, finding they can be non-zero in certain modified gravity scenarios, potentially affecting gravitational wave signals.

Contribution

It introduces a novel EFT approach to compute black hole TLNs with scalar profiles, showing non-zero values in non-stealth backgrounds like Hayward black holes.

Findings

Stealth Schwarzschild black holes have vanishing TLNs.

Hayward black holes exhibit non-zero TLNs and logarithmic running.

EFT framework allows for potential observational signatures in gravitational waves.

Abstract

We study static tidal Love numbers (TLNs) of a static and spherically symmetric black hole for odd-parity metric perturbations. We describe black hole perturbations using the effective field theory (EFT), formulated on an arbitrary background with a timelike scalar profile in the context of scalar-tensor theories. In particular, we obtain a static solution for the generalized Regge-Wheeler equation order by order in a modified-gravity parameter and extract the TLNs uniquely by analytic continuation of the multipole index $\ell$ to non-integer values. For a stealth Schwarzschild black hole, the TLNs are vanishing as in the case of Schwarzschild solution in general relativity. We also study the case of Hayward black hole as an example of non-stealth background, where we find that the TLNs are non-zero (or there is a logarithmic running). This result suggests that our EFT allows for non-vanishing TLNs and can in principle leave a detectable imprint on gravitational waves from inspiralling binary systems, which opens a new window for testing gravity in the strong-field regime.