Borel summation

Divergent series

Physics

Perturbation (astronomy)

Mathematics

Mathematical physics

Biology

Connection (principal bundle)

Anharmonicity

Analytic continuation

Mathematical analysis

Summation by parts

Series (stratigraphy)

Paleontology

Perturbation theory (quantum mechanics)

Geometry

Quantum mechanics

WKB approximation

Physical review. D/Physical review. D.

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-Schr\"odinger perturbation theory. The known WKB results are easily reproduced. Our analysis shows that the perturbative WKB series of the quasinormal frequencies turn out to be Borel summable divergent series both for the Schwarzschild and for the Reissner-Nordstr\"om black holes. Their Borel sums reproduce the correct numerical values.

Quasinormal modes of black holes and Borel summation