We propose a simple and efficient way to compute quasinormal frequencies of spherically symmetric black holes. We revisit an old idea that relates them to bound state energies of anharmonic oscillators by an analytic continuation. This connection enables us to achieve remarkable high-order computations of WKB series by Rayleigh–Schrödinger perturbation theory. The known WKB results are easily reproduced. Our analysis shows that the perturbative WKB series of the quasinormal frequencies turns out to be a Borel summable divergent series both for the Schwarzschild and for the Reissner–Nordström black holes. Their Borel sums reproduce the correct numerical values.

• Received 8 October 2019

DOI:https://doi.org/10.1103/PhysRevD.101.024008