Modified Teukolsky formalism: Null testing and numerical benchmarking

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 precitions for robust strong-field tests, with straightforward extensions to rotating backgrounds and coupling with matter fields.

Figures (6)

• Figure 1: Scaling test of the EFT-induced frequency shift for $\mathcal{O}_{5}$ and $\mathcal{O}_{8}$ at $\ell=2$. The left (right) panel shows the real (imaginary) part of the reduced quantity $\delta_{\rm Leaver}/\zeta^{2}$ as a function of the coupling $\zeta$. The near-constancy of these curves over a wide range of $\zeta$ indicates that the leading correction scales quadratically, $\delta_{\rm Leaver}\propto \zeta^{2}$. Deviations from flatness at the largest couplings signal the onset of non-asymptotic (higher-order) contributions beyond the leading power.
• Figure 2: Same as Fig. \ref{['fig:null58_l2']} but for $\ell = 3$.
• Figure 3: Same as Fig. \ref{['fig:null58_l2']} but for $\ell = 4$.
• Figure 4: Scaling test of the EFT frequency shift for $\mathcal{O}_{9}$ and $\mathcal{O}_{10}$ at $\ell=2$. The left (right) panel shows $\Re\!\left(\delta_{\rm Leaver}/\zeta\right)$ ($\Im\!\left(\delta_{\rm Leaver}/\zeta\right)$) versus the coupling $\zeta$. The near-flat behavior supports a leading linear dependence on $\zeta$, while departures at the largest $\zeta$ indicate the onset of higher-order contamination.
• Figure 5: Same as Fig. \ref{['fig:control910_l2']}, but for $\ell=3$.