Relativistic stars in Starobinsky gravity with the matched asymptotic expansions method

Abstract

We study the structure of relativistic stars in $\mathcal{R}+\alpha \mathcal{R}^{2}$ 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 $\alpha$, for uniform density stars. We obtain the mass-radius relations and study the dependence of maximum mass on $\alpha$. We find that $M_{\max}$ is almost linearly proportional to $\alpha$. For each $\alpha$ the maximum mass configuration has the biggest compactness parameter ($\eta = GM/Rc^2$), and we argue that the general relativistic stellar configuration corresponding to $\alpha=0$ is the least compact among these.