  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.

General Relativity and Quantum Cosmology