Computing spectral shifts for Johannsen-Psaltis Black Holes

TL;DR

This paper develops a method to compute spectral shifts in Johannsen-Psaltis black holes, revealing how beyond-GR modifications affect quasinormal modes and their parity properties, aiding precision tests of gravity with gravitational waves.

Contribution

It introduces a modified Teukolsky formalism combined with eigenvalue perturbation to calculate QNM spectral shifts in Johannsen-Psaltis black holes, exploring parity and isospectrality breaking.

Findings

Spectral shifts depend linearly on m for slow spins.

Johannsen-Psaltis black holes admit definite-parity modes.

Isospectrality between even and odd modes is broken at all spins.

Abstract

The growing number of gravitational wave (GW) detections and the increasing sensitivity of GW detectors have enabled precision tests of General Relativity (GR) in the strong-field regime. The recent observation of multiple quasinormal modes (QNMs) in GW250114 marks a major advance for observational black hole spectroscopy. This clear signal, together with the growing number of GW detections, highlights the need for accurate predictions of QNM spectra in beyond-GR theories in order to carry out precision searches for new physics. In this work, we continue to lay the foundation for such predictions using a modified Teukolsky formalism in conjunction with the eigenvalue perturbation method. We compute the spectral shifts of slowly rotating Johannsen-Psaltis black holes for $2 \leq \ell \leq 10$, all $m$, and overtones $n = 0, 1, 2$, and confirm the large-$\ell$ behavior of the modes by comparing with the WKB approximation. We find that these black holes admit definite-parity modes but break the isospectrality between even- and odd-parity QNMs at all spins, and that the shifts depend linearly on $m$ for slow spins. We further derive a general parity condition that any beyond-GR modification to the metric must satisfy to support definite-parity modes, providing new insights into isospectrality breaking and parity structure in gravitational perturbations.