Complex angular momentum in black hole physics and quasinormal modes

TL;DR

This paper uses the complex angular momentum method to analyze black hole quasinormal modes, revealing they are Breit-Wigner resonances linked to surface waves near the photon orbit, and constructs their spectrum via Regge trajectories.

Contribution

It introduces a novel approach connecting surface waves, Regge poles, and quasinormal modes in black hole physics using complex angular momentum techniques.

Findings

Quasinormal modes are Breit-Wigner resonances generated by surface waves.

Spectrum of quasinormal frequencies can be constructed from Regge trajectories.

Surface wave orbiting is a fundamental concept in black hole physics.

Abstract

By using the complex angular momentum approach, we prove that the quasinormal mode complex frequencies of the Schwarzschild black hole are Breit-Wigner type resonances generated by a family of surface waves propagating close to the unstable circular photon (graviton) orbit at $r=3M$. Furthermore, because each surface wave is associated with a given Regge pole of the $S$-matrix, we can construct the spectrum of the quasinormal-mode complex frequencies from Regge trajectories. The notion of surface wave orbiting around black holes thus appears as a fundamental concept which could be profitably introduced in various areas of black hole physics in connection with the complex angular momentum approach.