Black hole quasinormal mode excitation and mixing for coupled fields

Abstract

The idea of testing the nature of black holes and possible deviations from general relativity from their oscillation spectrum, known as ``black hole spectroscopy'', has become an experimental science. In many modified theories of gravity, the gravitational perturbations couple to additional degrees of freedom, leading to mode mixing and to a more complex ringdown signal. We adopt the parametrized quasinormal mode formalism for nonrotating black holes to study coupled perturbations in modified gravity theories in order to understand how the interaction with additional fields affects the quasinormal mode frequencies and their amplitudes. We compute the quasinormal mode spectrum of the coupled system in the frequency domain using direct integration and a matrix-valued continued-fraction method. We then compare the results with time-domain evolutions, where we extract the mode frequencies and amplitudes using the Prony method as well as least-squares fitting. In the weak-coupling regime, the scaling of the amplitudes associated with the gravitational-led and secondary-led modes can be understood perturbatively. The excitation of additional families of ringdown modes can become significant even when the frequency shifts remain moderate. We use our numerical time evolutions to provide ready-to-use coefficients for the mode amplitudes for representative initial data configurations. We work out specific examples, including dynamical Chern-Simons gravity and the special near-resonant case of coupled perturbations between the polar and axial quasinormal modes. Our theory-agnostic characterization of coupled systems should be useful to quantify systematic effects in black hole spectroscopy with next-generation gravitational-wave detectors.