Testing gravity with black hole ringdown amplitudes

Black hole ringdowns in extensions of general relativity (GR) generically exhibit two distinct signatures: i) theory-dependent shifts in the standard black-hole quasinormal modes, and ii) additional modes arising from extra fundamental fields-such as scalar, vector, or tensor degrees of freedom-that can also contribute to the gravitational-wave signal. As recently argued, in general both effects are present simultaneously, and accurately modeling them is essential for robust tests of GR in the ringdown regime. In this work, we investigate the impact of extra field-induced modes, which are often neglected in standard ringdown analyses, on the interpretation of gravitational-wave signals. To provide some concrete examples, we focus on dynamical Chern-Simons and Einstein-scalar-Gauss-Bonnet theories, well-motivated extensions of GR, characterized, respectively, by a parity-odd and a parity-even coupling between a dynamical scalar field and quadratic curvature invariants. We show that including extra field-induced modes improves the bounds on these theories compared to standard spectroscopy and also allows for equally constraining complementary tests not based on quasinormal mode shifts. Our analysis highlights the relevance of incorporating extra field-induced modes in ringdown templates and assesses their potential to either bias or enhance constraints on GR deviations.