Tidal Love Numbers from EFT of Black Hole Perturbations with Timelike Scalar Profile
Abstract
We study static tidal Love numbers (TLNs) of a static and spherically symmetric black hole for oddparity 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 scalartensor theories. In particular, we obtain a static solution for the generalized ReggeWheeler equation order by order in a modifiedgravity parameter and extract the TLNs uniquely by analytic continuation of the multipole index $\ell$ to noninteger 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 nonstealth background, where we find that the TLNs are nonzero (or there is a logarithmic running). This result suggests that our EFT allows for nonvanishing 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 strongfield regime.
 Publication:

arXiv eprints
 Pub Date:
 May 2024
 DOI:
 10.48550/arXiv.2405.10813
 arXiv:
 arXiv:2405.10813
 Bibcode:
 2024arXiv240510813B
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 40 pages