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.

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• Alternative gravity theories
• General relativity
• Gravitational waves