Klein-Gordon Oscillator with Scalar and Vector Potentials in Topologically Charged Ellis-Bronnikov type Wormhole

In this work, we study the Klein-Gordon oscillator with equal scalar and vector potentials in a topologically charged Ellis-Bronnikov wormhole space-time background. The behaviour of a relativistic oscillator field is studied with a position-dependent mass via transformation $M^{2}\rightarrow (M+S(x))^{2}$ and vector potential through a minimal substitution in the wave equation. Simplifying the Klein-Gordon oscillator equation for three different types of potential, such as linear confining, Coulomb-type, and Cornell-type potential and we arrive at a second-order differential equation known as the biconfluent Heun (BCH) equation and the corresponding confluent Heun function. Finally, we solve the wave equation by the Frobenius method as a power series expansion around the origin and obtain the energy levels and the wave function.