Parametrized Tidal Dissipation Numbers of Non-rotating Black Holes

TL;DR

This work provides the first theory-agnostic parametrization of black hole tidal dissipation numbers (TDNs) for static, non-rotating BHs. It extends the Mano-Suzuki-Takasugi (MST) formalism to deformed Regge-Wheeler/Zerilli equations with small potential corrections and uses Green's-function matching to connect horizon-ingoing near-zone perturbations to far-zone observables, allowing analytic extraction of TDNs to leading order in the orbital frequency. The key results express static Love numbers and TDNs in terms of deformation coefficients $\alpha_j^{\pm}$ and bases $e^{-,j}_{(0)}$, $e^{-,j}_{(1)}$ (and their even-parity analogs), making the formalism applicable to a broad class of theories, including EFTs with timelike scalar profiles, Einstein-Maxwell systems, and higher-curvature extensions of GR. The authors show the absence of logarithmic running at leading order and validate the framework across three applications, illustrating a practical path to constrain strong-field gravity with gravitational-wave observations.

Abstract

A set of tidal dissipation numbers (TDNs) quantifies the absorption of the tidal force exerted by a companion during an inspiralling phase of a binary compact object. This tidal dissipation generally affects the gravitational waveform, and measuring the TDNs of a black hole (BH) allows us to test the nature of gravity in the strong-field regime. In this paper, we develop a parametrized formalism for calculating the TDNs of static and spherically symmetric BH backgrounds using the Mano-Suzuki-Takasugi method, which connects the underlying perturbative equations with observable quantities in gravitational-wave observations in a theory-agnostic manner. Our formalism applies to any system where the master equation has the form of the Regge-Wheeler/Zerilli equation with a small correction to the effective potential. As an application of our formalism, we consider three examples: the effective field theory of BH perturbations with timelike scalar profile, the Einstein-Maxwell system, and a higher-curvature extension of general relativity. We also discuss the absence of logarithmic running for the TDNs.