The quasinormal modes of the rotating quantum corrected black holes

TL;DR

This work addresses how quantum gravity corrections alter black hole ringdowns by constructing rotating quantum corrected black holes (RQCBHs) via a Newman–Janis lift from a loop quantum gravity–motivated static solution and computing scalar QNMs using a hyperboloidal framework that turns the problem into a 2D eigenvalue problem. The QNM spectra, depending on $M$, $\bar{a}$, and $\bar{\alpha}$, are obtained with a two-dimensional pseudospectral method and then fitted with a bivariate rational function to enable GW-informed parameter estimation through pyRing. Applying the pipeline to events GW150914, GW190521, and GW231123 shows that inference on $M$ and $\bar{a}$ is significantly influenced by a strong coupling with $\bar{\alpha}$, even when the spectra are only mildly deviant from Kerr; this cautions against naive no-hair tests using $s=0$ QNMs. The authors advocate extending to $s=-2$ perturbations and perform hierarchical analyses across multiple events, noting that future detectors will enhance sensitivity to quantum-gravity-induced deviations in ringdowns.

Abstract

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 QNMs spectra problem into the two-dimensional eigenvalues problem, then the spectra are calculated by imposing two-dimensional pseudo-spectral method. Based on the resulting spectra, a parameter estimation pipeline for this RQCBH model with gravitational wave data is constructed by using \texttt{pyRing} in the ringdown phase. We find that, even when the RQCBH spectra exhibits a small deviation from the Kerr spectra, the strong correlation between the extra parameter coming from the quantum gravity theory and the intrinsic parameter of black hole may significantly affect the posterior distributions of the mass $M$ and the dimensionless spin $\bar{a}$.

Figures (5)

• Figure 1: Parameter space $(\alpha/M^2,a/M)$ for RQCBH. The red solid line corresponds to the extremal black holes with degenerate horizons. The sample green points which are used to obtain the QNMs spectra in the parameter space $(\alpha/M^2,a/M)$ corresponding to the points $(q,\kappa)$ in the $q-\kappa$ plane (see Fig. \ref{['parameter_region']}), in which these points are confined to the set $\{(q,\kappa)|0\le\kappa\le q\, ,q\le0.9\}$.
• Figure 2: The parameter space $(q,\kappa)$ for the RQCBH, where the feasible range of parameters is represented by shaded areas.
• Figure 3: The QNMs spectra for RQCBH with $\ell=3$, $m=2$ and $\ell=2$, $m=2$. The left top panel is the real part of the four "regular" modes. The right top panel is the imaginary part of the four "regular" modes. The left bottom panel is the real part of the four "mirror" modes. The right bottom is the imaginary part of the four "mirror" modes.
• Figure 4: The real (left) and imaginary (right) parts of QNMs spectra as functions of the dimensionless spin parameter $a/M$. The red circles and blue squares correspond to the Kerr QNMs spectra $_{0}\tilde{\omega}_{(2,2,0)}$ and $_{-2}\tilde{\omega}_{(2,2,0)}$, respectively. The black triangles represent the RQCBH mode $-\omega^{-}_{220}$ with the fixed parameter $\bar{\alpha}=0.1$.
• Figure 5: Posterior distributions of black hole parameters inferred from ringdown signals for $\mathrm{(i)}$GW150914 and $\mathrm{(ii)}$ GW190521, and $\mathrm{(iii)}$ GW231123. Left three panels: corner plots showing one-dimensional and two-dimensional posteriors of the mass $M$, spin $\bar{a}$, and the quantum correction parameter $\bar{\alpha}$ for the RQCBH model. Contours correspond to $68\%$ and $95\%$ credible regions, and vertical dashed lines indicate $16$th, $50$th, and $84$th percentiles. Right three panels: the comparison of posterior distribution of the mass $M$ and spin $\bar{a}$ between RQCBH (blue) coming from pyRing and standard Kerr BH (orange) coming from IMR analysis. The contours in the two-dimensional plots denote $68\%$ and $95\%$ credible regions.