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

We present the first precise calculations of the gravitational quasinormal-mode (QNM) frequencies for spinning black holes with dimensionless angular momenta $J\mathrm{/}{M}^2:=a\lesssim 0.75$ in dynamical Chern-Simons gravity. Using the $\mathit{\text{Metric}}\mathit{\text{pErTuRbations}}\mathit{\text{wIth}}\mathit{\text{speCtral}}\mathit{\text{methodS}}$ (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.