Anisotropic quark stars in $f(R)= R^{1+ε}$ gravity

Abstract: Within the metric formalism of $f(R)$ theories of gravity, where $R$ is the Ricci scalar, we study the hydrostatic equilibrium structure of compact stars with the inclusion of anisotropic pressure. In particular, we focus on the $f(R)= R^{1+\epsilon}$ model and we examine small deviations from General Relativity (GR) for $\vert \epsilon \vert \ll 1$. A suitable definition of mass function is explicitly formulated from the field equations and the value of the Ricci scalar at the center of each star is chosen such that it satisfies the asymptotic flatness requirement. We find that both the mass and the radius of a compact star are larger with respect to the general relativistic counterpart. Furthermore, we remark that the substantial changes due to anisotropy occur mainly in the high-central-density region.