On quasi-normal modes of Kerr black holes

TL;DR

This paper analytically calculates the asymptotic quasi-normal mode frequencies of Kerr black holes, providing a formula consistent with Hod's proposal and highlighting a frequency bound related to the black hole's angular momentum.

Contribution

It offers an analytical expression for quasi-normal mode frequencies of Kerr black holes for arbitrary wave spin, valid in the small angular momentum limit.

Findings

Frequency range is bounded by 1/a, where a is the black hole's angular momentum per unit mass.

Results agree with Hod's proposal based on Bohr's correspondence principle.

Analysis is valid primarily in the small-a (slow rotation) limit.

Abstract

We calculate analytically asymptotic values of quasi-normal frequencies of four-dimensional Kerr black holes by solving the Teukolsky wave equation. We obtain an expression for arbitrary spin of the wave in agreement with Hod's proposal which is based on Bohr's correspondence principle. However, the range of frequencies is bounded from above by $1/a$, where $a$ is the angular momentum per unit mass of the black hole. Our argument is only valid in the small-$a$ limit which includes the Schwarzschild case.