Asymptotic Spectroscopy of Rotating Black Holes

TL;DR

This paper analytically computes the asymptotic resonant frequencies of rotating black holes, including quasinormal modes, by connecting wave amplitudes to semiclassical bound states in a complexified potential.

Contribution

It introduces an analytical method to determine the asymptotic resonant modes of rotating black holes using complex analysis and semiclassical approximations.

Findings

Identifies resonant modes with semiclassical bound states.

Relates modes to characteristic temperatures and chemical potentials.

Provides insights into the microscopic structure of black holes.

Abstract

We calculate analytically the transmission and reflection amplitudes for waves incident on a rotating black hole in d=4, analytically continued to asymptotically large, nearly imaginary frequency. These amplitudes determine the asymptotic resonant frequencies of the black hole, including quasinormal modes, total-transmission modes and total-reflection modes. We identify these modes with semiclassical bound states of a one-dimensional Schrodinger equation, localized along contours in the complexified r-plane which connect turning points of corresponding null geodesics. Each family of modes has a characteristic temperature and chemical potential. The relations between them provide hints about the microscopic description of the black hole in this asymptotic regime.