Year: 2018
Type: article
Abstract: We investigate boson star (BS) solutions in the Einstein-Proca theory with the quartic order self-interaction of the vector field $\ensuremath{\lambda}({A}^{\ensuremath{\mu}}{\overline{A}}_{\ensuremath{\mu}}{)}^{2}/4$ and the mass term $\ensuremath{\mu}{\overline{A}}^{\ensuremath{\mu}}{A}_{\ensuremath{\mu}}/2$, where ${A}_{\ensuremath{\mu}}$ is the complex vector field and ${\overline{A}}_{\ensuremath{\mu}}$ is the complex conjugate of ${A}_{\ensuremath{\mu}}$, and $\ensuremath{\lambda}$ and $\ensuremath{\mu}$ are the coupling constant and the mass of the vector field, respectively. The vector BSs are characterized by the two conserved quantities, the Arnowitt-Deser-Misner (ADM) mass and the Noether charge associated with the global $U(1)$ symmetry. We show that in comparison with the case without the self-interaction $\ensuremath{\lambda}=0$, the maximal ADM mass and Noether charge increase for $\ensuremath{\lambda}>0$ and decrease for $\ensuremath{\lambda}<0$. We also show that there exists the critical central amplitude of the temporal component of the vector field above which there is no vector BS solution, and for $\ensuremath{\lambda}>0$ it can be expressed by the simple analytic expression. For a sufficiently large positive coupling $\mathrm{\ensuremath{\Lambda}}\ensuremath{\mathrel{:=}}{M}_{\mathrm{pl}}^{2}\ensuremath{\lambda}/(8\ensuremath{\pi}{\ensuremath{\mu}}^{2})\ensuremath{\gg}1$, the maximal ADM mass and Noether charge of the vector BSs are obtained from the critical central amplitude and of $\mathcal{O}[\sqrt{\ensuremath{\lambda}}{M}_{\mathrm{pl}}^{3}/{\ensuremath{\mu}}^{2}\mathrm{ln}(\ensuremath{\lambda}{M}_{\mathrm{pl}}^{2}/{\ensuremath{\mu}}^{2})]$, which is different from that of the scalar BSs, $\mathcal{O}(\sqrt{{\ensuremath{\lambda}}_{\ensuremath{\phi}}}{M}_{\mathrm{pl}}^{3}/{\ensuremath{\mu}}_{\ensuremath{\phi}}^{2})$, where ${\ensuremath{\lambda}}_{\ensuremath{\phi}}$ and ${\ensuremath{\mu}}_{\ensuremath{\phi}}$ are the coupling constant and the mass of the complex scalar field.
Author: Masato Minamitsuji
Institutions: University of Lisbon, Instituto Superior Técnico
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2803279172