The quasinormal modes (QNMs) of a rotating quantum corrected black hole (RQCBH) are studied by employing the hyperboloidal framework for the scalar perturbation. This framework is used to cast the QNM spectra problem into a two-dimensional eigenvalue problem, then the spectra are calculated by imposing the two-dimensional pseudospectral method. Based on the resulting scalar spectra, a parameter estimation pipeline for this RQCBH model with gravitational wave data is constructed by using pyring in the ringdown phase. We use informative priors in our inference that incorporates the mass and spin distributions predicted by the inspiral-merger phase as the prior distributions for the ringdown analysis. Notably, since the waveform model beyond the Kerr black hole in pyring is designed for the tensor perturbation, the inferred posterior distributions should be interpreted as a methodological investigation rather than as physical constraints from observations. The methodological results show that the use of informative priors consistently yields a tighter posterior on the quantum correction parameter compared to analyses without such priors, and the spin inferred from the RQCBH model begins to be significant and differs from that of the Kerr model. This opens a promising avenue for testing quantum-gravity-induced deviations using gravitational-wave spectroscopy.

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• Alternative gravity theories
• Gravitational waves
• Loop quantum gravity