Quasinormal modes of generalized P\"oschl-Teller potentials

TL;DR

This paper employs algebraic methods to derive quasinormal modes and frequencies for generalized P"oschl-Teller potentials, revealing stable dynamics without late-time tails.

Contribution

It introduces an algebraic approach using Lie algebra sl(2) to analytically compute quasinormal modes for generalized P"oschl-Teller potentials.

Findings

Derived explicit quasinormal mode spectra.

Established stability and absence of late-time tails.

Connected algebraic structures to wave dynamics.

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.