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 $2\le \ell \le 10$, all $m$, and overtones $n=0,1,2$, and confirm the large-$\ell$ behavior of the modes by comparing with the Wentzel-Kramers-Brillouin 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 in order to support definite-parity modes, providing new insights into isospectrality breaking and parity structure in gravitational perturbations.

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• Alternative gravity theories
• Classical black holes
• Gravitational waves