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2018

Vector boson star solutions with a quartic order self-interaction

Minamitsuji, Masato

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We investigate boson star (BS) solutions in the Einstein-Proca theory with the quartic order self-interaction of the vector field $\lambda (A^\mu\bar{A}_\mu)^2/4$ and the mass term $\mu \bar{A}^\mu A_\mu/2$, where $A_\mu$ is the complex vector field and ${\bar A}_\mu$ is the complex conjugate of $A_\mu$, and $\lambda$ and $\mu$ 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 $\lambda=0$, the maximal ADM mass and Noether charge increase for $\lambda>0$ and decrease for $\lambda<0$.
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 $\lambda>0$ it can be expressed by the simple analytic expression.

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