Nonperturbative models of quark stars in $f(R)$ gravity

TL;DR

This paper models quark stars within nonperturbative $f(R)$ gravity, analyzing their mass-radius relations, fine-tuning requirements, and potential observational differences from General Relativity, especially via gravitational redshift.

Contribution

It introduces nonperturbative $f(R)$ gravity models for quark stars, explores the fine-tuning of scalar curvature, and compares predictions with scalar-tensor theories and General Relativity.

Findings

Mass of quark stars increases with $\alpha$ in $f(R)$ gravity.

Fine-tuning of scalar curvature $R$ is necessary for solutions.

Gravitational redshift can distinguish modified gravity from GR.

Abstract

Quark star models with realistic equation of state in nonperturbative $f(R)$ gravity are considered. The mass-radius relation for $f(R)=R+\alpha R^2$ model is obtained. Considering scalar curvature $R$ as an independent function, one can find out, for each value of central density, the unique value of central curvature for which one has solutions with the required asymptotic $R\rightarrow 0$ for $r\rightarrow\infty$. In another words, one needs a fine-tuning for $R$ to achieve quark stars in $f(R)$ gravity. We consider also the analogue description in corresponding scalar-tensor gravity. The fine-tuning on $R$ is equivalent to the fine-tuning on the scalar field $\phi$ in this description. For distant observers, the gravitational mass of the star increases with increasing $\alpha$ ($\alpha>0$) but the interpretation of this fact depends on frame where we work. Considering directly $f(R)$ gravity, one can say that increasing of mass occurs by the "gravitational sphere" outside the star with some "effective mass". On the other hand, in scalar-tensor theory, we also have a dilaton sphere (or "disphere") outside the star but its contribution to gravitational mass for distant observer is negligible. We show that it is possible to discriminate modified theories of gravity from General Relativity due to the gravitational redshift of the thermal spectrum emerging from the surface of the star.