Tidal response beyond vacuum general relativity with a canonical definition

Tidal effects on compact objects provide profound theoretical insights into the structure of the field equations, and are wonderful probes of the equation of state of matter, of the nature of black holes, and of the underlying theory of gravity. The natural framework for understanding tides is a perturbative scheme. Here, we point out ambiguities in determining tidal response functions within such a framework, which may lead to bias in constraining physical parameters with gravitational-wave observations if the computed quantities are not properly linked to observables. We propose a canonical tidal response function definition to compare values of tides in theories beyond vacuum general relativity in a unified manner. As an example, we provide black hole tidal response functions, including both conservative and dissipative pieces, in various theories of gravity. Tidal dissipation Love numbers for black holes are derived here for the first time in most of the non-Einsteinian theories considered in this paper.