Relativistic stars in Starobinsky gravity with the matched asymptotic expansions method
We study the structure of relativistic stars in $\mathcal{R}+α\mathcal{R}^{2}$ theory using the method of matched asymptotic expansion to handle the higher order derivatives in field equations arising from the higher order curvature term. We find solutions, parametrized by $α$, for uniform density stars. We obtain the mass-radius relations and study the dependence of maximum mass on $α$. We find that $M_{\max}$ is almost linearly proportional to $α$. For each $α$ the maximum mass configuration has the biggest compactness parameter ($η= GM/Rc^2$), and we argue that the general relativistic stellar configuration corresponding to $α=0$ is the least compact among these.
gr-qc↗