Optimal convergence rate to the nonrelativistic limit of Chandrasekhar variational model for Neutron stars

TL;DR

This paper establishes the optimal convergence rate of the Chandrasekhar variational model for neutron stars to its nonrelativistic limit as the speed of light increases, including convergence of minimizers and support radii.

Contribution

It introduces a novel approach to determine the optimal convergence rate of order 1/c^2 for the model's minimizers and support radii in the nonrelativistic limit.

Findings

Convergence rate of minimizers is 1/c^2.

Support radii difference is O(1/c^2).

Uniform bounds of radii and density are obtained.

Abstract

In this paper, we consider the nonrelativistic limit of Chandrasekhar variational model for neutron stars. We show that the minimizer $\rho_{c}$ of Chandrasekhar energy $E_c(N)$ converges strongly to the minimizer $\rho_{\infty}$ of limit energy $E_{\infty}(N)$ in $L^1\cap L^{\frac{5}{3}}(\mathbb{R}^3)$ as the speed of light $c\rightarrow\infty$, this is a limit between two free boundary problems. Moreover, we develop a novel approach to obtain the convergence rates, we show that the above nonrelativistic limit has the optimal convergence rate $\frac{1}{c^2}$. For the radius $R_c$ of the compact support of $\rho_c(x)$ and the radius $R_\infty$ of the compact support of $\rho_\infty(x)$, we also get the optimal convergence rate $\frac{1}{c^2}$, this means that $R_\infty-R_c=O(\frac{1}{c^2})$ as $c\rightarrow\infty$. Moreover, we also obtain the optimal uniform bounds of $R_c$ and $L^\infty$-norm of $\rho_c$ with respect to $N$ as $c\rightarrow \infty$.