Analytic quasinormal frequencies of the Casadio–Fabbri–Mazzacurati black hole

We present analytic approximations for the quasinormal modes of scalar, Dirac, and electromagnetic perturbations of brane-world black holes, specifically those described by the widely known Casadio–Fabbri–Mazzacurati solution. We compare these analytical approximations with results obtained through time-domain integration and the sixth order Wentzel–Kramers–Brillouin method with Padé approximants. Our analysis reveals that for ℓ > 0, the derived concise analytic expressions align well with the aforementioned computational methods. In the eikonal limit we show that the correspondence between the null geodesics and high frequency quasinormal modes holds. The obtained analytic formulas are further used to test the Hod’s upper bound on the damping rate of the fundamental frequency.