Equation of State of Neutron Stars with Junction Conditions in the Starobinsky Model

Understand

We study the Starobinsky or $R^2$ model of $f(R)=R+\alpha R^2$ for neutron stars with the structure equations represented by the coupled differential equations and the \emph{polytropic} type of the matter equation of state.

• The junction conditions of $f(R)$ gravity are used as the boundary conditions to match the Schwarschild solution at the surface of the star.
• Based on these the conditions, we demonstrate that the coupled differential equations can be solved \emph{directly}.
• In particular, from the dimensionless equation of state $\bar{\rho} = \bar{k}\, \bar{p}^{\,\gamma}$ with $\bar{k}\sim5.0$ and $\gamma\sim0.75$ and the constraint of $\alpha\lesssim {1.47722}\times 10^{7}\, \text{m}^2$, we obtain the \emph{minimal} mass of the NS to be around 1.44 $M_{\odot}$.