Scalar Bosons with Position-Dependent Mass in a (2+1)-Dimensional Gravitational Wave Background

Abstract

In this study, we examine the dynamics of relativistic scalar bosons with a position-dependent mass profile, m(r), in a (2+1)-dimensional gravitational wave background. We derive the Klein-Gordon equation describing this system and obtain exact solutions by incorporating a Coulomb-like modification, m(r)-> m-alpha/r. Our analysis reveals that significantly different behaviors can emerge, dictated by the critical value of the coupling parameter alpha. Specifically, the system exhibits either stable oscillatory modes or decays without real oscillations, depending on the value of alpha. Furthermore, we demonstrate that such a scalar boson cannot exist over time when the coupling parameter reaches its critical value, alpha c.