Modified black-hole perturbation formalism: Null testing and numerical benchmarking
Phys. Rev. D 114, 024077 – Published 28 July, 2026
DOI: https://doi.org/10.1103/w112-1pnj
Abstract
Next-generation gravitational-wave detectors will make black-hole ringdown an increasingly sensitive probe of small departures from General Relativity in the strong-field regime. This motivates obtaining high-precision predictions of gravitational effective field theory, as spectral shifts can be quite small. Here we perform a focused stress test of a modified black-hole perturbation framework by designing two null diagnostics. First, we consider an action with redundant operators that must produce zero first-order vacuum QNM shifts. Second, we exploit a Ricci-flat identity relating two physical cubic Riemann theories to test such a relation is satisfied by the ringdown spectra obtained. We compute the shifts using two independent numerical approaches; the eigenvalue-perturbation and generalized continued-fraction (Leaver-type) methods. Both null tests are passed across multiple multipoles and overtones, and the control-operator results agree in magnitude with the benchmark values reported in Ref. [1]. These validations support using this modified black-hole perturbation framework for obtaining accurate predictions for robust strong-field tests, with straightforward extensions to rotating backgrounds and coupling with matter fields.
