  Our research aims to investigate how the gravitational field influences the
spectroscopic structure of the Feshbach-Villars oscillator in G\"urses
space-time. To achieve this, we utilize the first-order Feshbach-Villars
version of the Klein-Gordon equation, which is a relativistic wave equation for
spinless particles. We examine the oscillator's quantum mechanical behavior in
the presence of a Coulomb-type potential, and calculate the resulting wave
functions and energy levels for both free and interacting scenarios. In
addition, we study the interaction between the Coulomb-type potential and
G\"urses space-time affects the Feshbach-Villars oscillator's behavior,
specifically with regard to its spectroscopic structure. This study has
important implications for our understanding of the interplay between quantum
mechanics, relativity, and gravitational fields at the microscopic level.
