Damped modes for a bosonic quantum oscillator in the near-horizon geometry of the BTZ black hole

We analyse the evolution of a generalized bosonic oscillator in the near horizon geometry of the BTZ black hole by analytically obtaining a solution of the associated Klein-Gordon equation. We show that it is possible to obtain relativistic frequency expression in closed-form for the system in question. Here, we observe that such a system decays in time without any real oscillation and the damped modes depend explicitly on the parameters of the oscillator coupling besides the parameters of the background geometry. This result allows us to analyse the influences of both oscillator coupling and spacetime parameters on the evolution of such a test field. Also, the results indicate that the spacetime background is stable under this perturbation field.