Vector boson oscillator in the near-horizon of the BTZ black hole

We investigate the interaction of a generalized vector boson oscillator with the near-horizon geometry of the Bañados–Teitelboim–Zanelli (BTZ) black hole and try to determine the corresponding quasibound state frequencies. To do this, we seek an analytical solution of the relativistic vector boson equation, derived as an excited state of Zitterbewegung, with Cornell-type non-minimal coupling in the near-horizon geometry of the BTZ black hole. The vector boson equation includes a symmetric spinor of rank two and this allows to obtain an analytical solution of the corresponding equation. By imposing appropriate boundary conditions, we show that it is possible to arrive at a relativistic frequency (ω) expression in the form of ω=ωRe+ωIm . Our results show that real ( ∝ωRe ) and damped ( ∝1|ωIm| ) oscillations depend on the parameters of the background geometry, coefficients of the non-minimal coupling and strength of the oscillator. This allows us to analyse the effects of both non-minimal coupling and spacetime parameters on the evolution of the considered vector field. We discuss the results in details and see also that the background is stable under the perturbation field in question.