Revisiting compact star in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> gravity: Roles of chameleon potential and energy conditions
Kota Numajiri, Yong-Xiang Cui, Taishi Katsuragawa, Shin’ichi Nojiri
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 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.