Parametrized Love numbers of non-rotating black holes

TL;DR

This paper introduces a parametrized, theory-agnostic framework to compute and classify black hole Love numbers, which are crucial for testing gravity theories through gravitational wave observations.

Contribution

It develops a formalism connecting black hole Love numbers with observable gravitational-wave quantities in a theory-independent manner.

Findings

Computed Love numbers for various black hole systems.

Classified black hole Love numbers as vanishing, nonzero, or scale-dependent.

Validated the formalism with analytic and numerical results.

Abstract

A set of tidal Love numbers quantifies tidal deformation of compact objects and is a detectable imprint in gravitational waves from inspiralling binary systems. The measurement of black hole Love numbers allows to test strong-field gravity. In this paper, we present a parametrized formalism to compute the Love numbers of static and spherically symmetric black hole backgrounds, connecting the underlying equations of a given theory with detectable quantities in gravitational-wave observations in a theory-agnostic way. With this formalism, we compute the Love numbers in several systems. We further classify black hole Love numbers according to whether they vanish, are nonzero, or are ``running'' (scale-dependent), in theories or backgrounds that deviate perturbatively from the GR values. The construction relies on static linear perturbations and scattering theory. Our analytic and numerical results are in excellent agreement. As a side result, we show how to use Chandrasekhar's relations to relate basis of even parity to odd parity.