Speaker: Takuya Katagiri (Tohoku U.)
Title: Ladder operators and quasinormal modes in Banados-Teitelboim-Zanelli black holes
Abstract: Ladder operators are useful tools that provide a deep insight into a system. For example, in quantum mechanics, they change a quantum number of solutions of the Schrodinger equation and allow for relating the different eigenstates without detailed knowledge of the solutions. It is known that the ladder operators in quantum mechanics are related to the underlying symmetry of a given system.
In this talk, I will report our recent work about the application of ladder operators to black hole physics. In this work, we study quasinormal modes (QNMs) of massive Klein-Gordon fields in static Banados-Teitelboim-Zanelli (BTZ) black holes in terms of ladder operators constructed from spacetime conformal symmetries. Because the BTZ spacetime is locally isometric to three-dimensional anti-de Sitter spacetimes, 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. 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.
Date & Time: 3:00 PM, Aug 3, 2022.