Parametrized Tidal Dissipation Numbers of Non-rotating Black Holes

TL;DR

This paper introduces a parametrized approach to calculate tidal dissipation numbers of non-rotating black holes, enabling tests of gravity theories through gravitational-wave data analysis.

Contribution

It develops a theory-agnostic formalism for computing TDNs of static, spherically symmetric black holes using the Mano-Suzuki-Takasugi method, applicable to various gravity models.

Findings

Formalism applies to master equations similar to Regge-Wheeler/Zerilli.

Demonstrated with examples from effective field theory, Einstein-Maxwell, and higher-curvature gravity.

Discussed the non-existence of logarithmic running in TDNs.

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.