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

• Published in: arXiv.org 2023-11
• Main Authors: Pretel, Juan M Z, Jorás, Sergio E, Reis, Ribamar R R, Duarte, Sergio B, Arbañil, José D V
• Format: Article
• Language: English
• Subjects: Binding energy; Density; Equations of state; Mathematical analysis; Neutron stars; Scalars; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2308.00203

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 \(\phi\) and coupling function \(\Phi(\phi)= \exp[2\phi/\sqrt{3}]\), we investigate the hydrostatic equilibrium structure of neutron stars for the simple potential \(V(\phi)= \omega\phi^2/2\) 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 \(\omega\) 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 \(dM/d\rho_c^J = 0\) on the \(M(\rho_c^J)\)-curve.