The Lieb-Yau Conjecture for Ground States of Pseudo-Relativistic Boson Stars

Abstract

It is known that ground states of the pseudo-relativistic Boson stars exist if and only if the stellar mass $N>0$ satisfies $N<N^{\ast }$, where the finite constant $N^{\ast }$ is called the critical stellar mass. Lieb and Yau conjecture in [Comm. Math. Phys., 1987] that ground states of the pseudo-relativistic Boson stars are unique for each $N<N^{\ast }$. In this paper, we prove that the above uniqueness conjecture holds for the particular case where $N>0$ is small enough.

22 pages, any comments are welcome