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

Abstract

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 $\varphi$ and coupling function $\Phi (\varphi )=\exp [2\varphi /\sqrt{3}]$, we investigate the hydrostatic equilibrium structure of neutron stars for the simple potential $V(\varphi )=\omega {\varphi }^2/2$ 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.

9 pages, 6 figures. Accepted for publication in Physics of the Dark Universe

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