Modified Teukolsky formalism: Null testing and numerical benchmarking

TL;DR

This paper rigorously tests a modified Teukolsky formalism for black-hole ringdown predictions, validating its accuracy and consistency through null diagnostics and numerical methods, supporting its use in strong-field gravity tests.

Contribution

It introduces null diagnostics and numerical validation methods to verify the accuracy of the modified Teukolsky framework for gravitational wave predictions.

Findings

Null tests are passed across multiple multipoles and overtones.

Numerical approaches agree with benchmark values.

Framework validated for accurate strong-field gravity predictions.

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 the modified-Teukolsky 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 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 the framework for obtaining accurate predictions for robust strong-field tests, with straightforward extensions to rotating backgrounds and coupling with matter fields.