Behavior of spin-0 scalar particles in Eddington-inspired Born-Infeld gravity global monopole with harmonic oscillator potential
Abstract
In this paper, we investigate the behavior of a scalar bosonic field within the backdrop of Eddington-inspired Born-Infeld gravity with a global monopole configuration. Additionally, we consider the presence of both scalar and vector potentials. To introduce the scalar potential, we perform a transformation on the mass term, replacing M2 with (M+S)2. For the vector potential, we apply a minimal coupling scheme, transforming p mu -> D mu equivalent to(p mu-eA mu) within the relativistic Klein-Gordon equation. We opt for a harmonic oscillator scenario where the scalar and vector potentials are equal, i.e. S=V proportional to x2. Through this setup, we analytically solve the wave equation using the confluent Heun equation form. Subsequently, we delve into the quantum system in the absence of any potential, determining the permissible values for bound-state relativistic energy levels and the scalar field's wave function. Our analysis reveals that the energy levels and wave function are influenced by various parameters present in the eigenvalue expression.
