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 ($\eta =GM/R{c}^2$), and we argue that the general relativistic stellar configuration corresponding to $\alpha =0$ is the least compact among these.

• Received 15 April 2016

DOI:https://doi.org/10.1103/PhysRevD.96.084040