Revisiting compact star in $F(R)$ gravity: Roles of chameleon potential and energy conditions

TL;DR

This paper investigates the structure of compact stars in $F(R)$ gravity, emphasizing the role of the chameleon potential and scalar fields, and refines previous models by analyzing scalar-hair and mass-radius relations.

Contribution

It provides a detailed numerical analysis of scalar-field profiles in $F(R)$ gravity, clarifies the scalar-hair problem, and highlights the impact of the chameleon potential on star properties.

Findings

Scalar field often acts as a quintessential field reducing star mass.

Chameleon potential is crucial for scalar-field configuration inside stars.

Refined external geometry analysis resolves previous scalar-hair issues.

Abstract

We reexamine the static and spherical symmetric compact star configuration in the $R^2$ model of the $F(R)$ gravity theory. With asymptotic solutions for the additional scalar degrees of freedom, we refine analysis on the external geometry and settle the scalar-hair problem argued in previous works. Performing the numerical integration of the modified Tolman-Oppenheimer-Volkoff equations as a two-boundaries-value problem, we further discuss the scalar-field distribution inside the compact stars and its influence on the mass-radius relation. We show that the chameleon potential plays an essential role in determining the scalar-field profile inside the star. The scalar field often behaves as a quintessential field that effectively decreases the mass of compact stars with lower central energy density.