Quasinormal modes of the BTZ black hole are generated by surface waves supported by its boundary at infinity

Abstract

We develop the complex angular momentum method in the context of the BTZ black hole physics. This is achieved by extending a formalism introduced a long time ago by Arnold Sommerfeld, which allows us to define and use the Regge pole concept in a framework where the notion of an $S$ matrix does not exist. The Regge poles of the BTZ black hole are exactly obtained and from the associated Regge trajectories we determine its quasinormal mode complex frequencies. Furthermore, our approach permits us to physically interpret them: they appear as Breit-Wigner-type resonances generated by surface waves supported by the black hole boundary at infinity which acts as a photon sphere.