Searching for Non-Kerr Dynamical Degrees of Freedom in Black Hole Ringdowns

The ringdown following a black hole merger is commonly described as a superposition of Kerr quasinormalmodes (QNMs), whose complex frequencies are determined by the mass and spin of the remnant black hole,and is therefore used to test general relativity in the strong-field regime. Conventional black holespectroscopy has focused primarily on shifts in Kerr QNM frequencies. However, if an additional field isnonminimally coupled to gravity, the field’s own characteristic frequencies may contaminate thegravitational-wave signal, so an analysis that allows only for frequency shifts may miss an important classof signatures. This paper proposes a unified framework for comparing: (i) shifts in Kerr-mode frequenciesand damping rates; (ii) contamination by additional modes associated with scalar or other fields; (iii)standard or already known nonstationary components, including nonlinear QNMs, prompt response, tails,and memory; and (iv) correlations between formation history and residual complex frequencies afterconditioning on the remnant mass and spin. The central distinction is that formation history is alreadyexpected, within general relativity, to affect QNM amplitudes and phases, whereas a systematic dependenceof sufficiently late-time eigenfrequencies on formation history would constitute a distinct test of the usualKerr final-state hypothesis. We introduce an “equivalent-remnant comparison,” in which events with similarremnant mass and spin but different formation histories are compared; a time-window stability test in whichthe ringdown start time is varied; a hierarchical multi-event analysis; and explicit falsification criteria. Theproposal does not claim the detection of an unknown force or a material property of spacetime. It is aminimal test design for using black holes as discriminating detectors of otherwise hidden dynamical degreesof freedom.