Ground states of pseudo-relativistic boson stars under the critical stellar mass

Guo, Yujin; Zeng, Xiaoyu

doi:10.1016/j.anihpc.2017.04.001

Guo, Yujin ; Zeng, Xiaoyu

Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 6, pp. 1611-1632.

Résumé

We consider ground states of pseudo-relativistic boson stars with a self-interacting potential $K (x)$ in $R^{3}$ , which can be described by minimizers of the pseudo-relativistic Hartree energy functional. Under some assumptions on $K (x)$ , minimizers exist if the stellar mass N satisfies $0 < N < N^{⁎}$ , and there is no minimizer if $N > N^{⁎}$ , where $N^{⁎}$ is called the critical stellar mass. In contrast to the case of the Coulomb-type potential where $K (x) \equiv 1$ , we prove that the existence of minimizers may occur at $N = N^{⁎}$ , depending on the local profile of $K (x)$ near the origin. When there is no minimizer at $N = N^{⁎}$ , we also present a detailed analysis of the behavior of minimizers as N approaches $N^{⁎}$ from below, for which the stellar mass concentrates at a unique point.

MR Zbl

DOI : 10.1016/j.anihpc.2017.04.001

Mots clés : Ground states, Boson stars, Mass concentration, Critical mass

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     title = {Ground states of pseudo-relativistic boson stars under the critical stellar mass},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1611--1632},
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Guo, Yujin; Zeng, Xiaoyu. Ground states of pseudo-relativistic boson stars under the critical stellar mass. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 6, pp. 1611-1632. doi : 10.1016/j.anihpc.2017.04.001. http://www.numdam.org/articles/10.1016/j.anihpc.2017.04.001/

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