The existence of relativistic stars in f(R) gravity

TL;DR

This paper demonstrates that relativistic stars can exist in f(R) gravity, showing stable configurations with deep potentials and analyzing the effects of chameleon screening, contrasting with prior claims that such stars cannot exist.

Contribution

The study provides numerical evidence of stable relativistic stars in f(R) gravity and clarifies the role of chameleon effects and maximum gravitational potentials, refuting previous assertions.

Findings

Stable relativistic stars exist in f(R) gravity.

Chameleon effects screen star mass and stabilize gravity.

Maximum gravitational potential in f(R) is slightly lower than in GR.

Abstract

We refute recent claims in the literature that stars with relativistically deep potentials cannot exist in $f(R)$ gravity. Numerical examples of stable stars, including relativistic ($GM_\star/r_\star \sim 0.1$), constant density stars, are studied. As a star is made larger, non-linear "chameleon" effects screen much of the star's mass, stabilizing gravity at the stellar center. Furthermore, we show that the onset of this chameleon screening is unrelated to strong gravity. At large central pressures $P>\rho/3$, $f(R)$ gravity, like general relativity, does have a maximum gravitational potential, but at a slightly smaller value: $GM_\star/r_\star = 0.345 < 4/9$ for constant density and one choice of parameters. This difference is associated with negative central curvature $R$ under general relativity not being accessed in the $f(R)$ model, but does not apply to any known astrophysical object.