Quasinormal modes of generalized P\"oschl-Teller potentials

Abstract

Using algebraic techniques we obtain quasinormal modes and frequencies associated to generalized forms of the scattering P\"oschl-Teller potential. This approach is based on the association of the corresponding equations of motion with Casimir invariants of differential representations of the Lie algebra sl(2). In the presented development, highest weight representations are constructed and fundamental states are calculated. An infinite tower of quasinormal mode solutions is obtained by the action of a lowering operator. The algebraic results are used in the analysis of the Cauchy initial value problem associated to the generalized P\"oschl-Teller potentials. For the scattering potentials considered, there are no late-time tails and the dynamics is always stable.