Ladder operators and quasinormal modes in Bañados-Teitelboim-Zanelli black holes

Abstract

We study quasinormal modes (QNMs) of massive Klein-Gordon fields in static Bañados-Teitelboim-Zanelli (BTZ) black holes in terms of ladder operators constructed from spacetime conformal symmetries. Because the BTZ spacetime is locally isometric to the three-dimensional anti-de Sitter spacetime, ladder operators, which map a solution of the massive Klein-Gordon equation into that with different mass squared, can be constructed from spacetime conformal symmetries. In this paper, we apply the ladder operators to the QNMs of the Klein-Gordon equations in the BTZ spacetime. We demonstrate that the ladder operators can change indices of QNM overtones, and all overtone modes can be generated from a fundamental mode when we impose the Dirichlet or Neumann boundary condition at infinity. We also discuss the case with the Robin boundary condition.

Quasinormal modes of charged BTZ black holes

“…The quasinormal frequencies in BTZ black holes were widely studied in the past years [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] with many different purposes. They were analytically calculated for the first time in the non-rotating black hole in [47].…”