Some exact relativistic star solutions in $f(R)$ gravity

We present a covariant description of non-vacuum static spherically symmetric spacetimes in $f(R)$ gravity applying the (1+1+2) covariant formalism. The propagation equations are then used to derive a covariant and dimensionless form of the Tolman-Oppenheimer-Volkoff (TOV) equations. We then give a solution strategy to these equations and obtain some new exact solutions for the particular case $f(R)=R+\alpha R^2$, which have the correct thermodynamic properties for standard matter.