Quasinormal mode frequencies and gravitational perturbations of spinning black holes in modified gravity through METRICS: The dynamical Chern-Simons gravity case

Abstract

We present the first precise calculations of the gravitational quasinormal-mode (QNM) frequencies for spinning black holes with dimensionless angular momenta $J/M^2:=a\lesssim 0.75$ in dynamical Chern-Simons gravity. Using the \textit{Metric pErTuRbations wIth speCtral methodS} (METRICS) framework, we compute the QNM frequencies of both axial and polar metric perturbations, focusing on the $nlm=022$, $033$, and $032$ modes. The METRICS frequencies for the 022 mode achieve numerical uncertainties $\lesssim 10^{-4}$ when $0\le a\le 0.5$ and $\lesssim 10^{-3}$ for $0.5\le a\le 0.75$, without decoupling or simplifying the linearized field equations. We also derive optimal fitting polynomials to enable efficient and accurate evaluations of the leading-order frequency shifts in these modes. The METRICS frequencies and fitting expressions are a robust and indispensable step toward enabling gravitational-wave ringdown tests of dynamical Chern-Simons gravity.

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