Compact stars in scalar–tensor theories with a single-well potential and the corresponding f(R) theory

The macroscopic properties of compact stars in modified gravity theories can be significantly different from the general relativistic (GR) predictions. Within the gravitational context of scalar–tensor theories, with a scalar field ϕ and coupling function Φ(ϕ)=exp[2ϕ/3], we investigate the hydrostatic equilibrium structure of neutron stars for the simple potential V(ϕ)=ωϕ²/2 defined in the Einstein frame (EF). From the scalar field in the EF, we also interpret such theories as f(R) gravity in the corresponding Jordan frame (JF). The mass–radius relations, proper mass, and binding energy are obtained for a polytropic equation of state (EoS) in the JF. Our results reveal that the maximum-mass values increase substantially as ω gets smaller, while the radius and mass decrease in the low-central-density region as we move further away from the pure GR scenario. Furthermore, a cusp is formed when the binding energy is plotted as a function of the proper mass, which indicates the appearance of instability. Specifically, we find that the central-density value where the binding energy is a minimum corresponds precisely to dM/dρ_c^J=0 on the M(ρ_c^J)-curve.