We study the transition of charged boson stars from sub- to super-criticality. This transition is defined as that choice of coupling constants for which the Coulomb repulsion of two individual bosons (that make up the star) exactly cancels their gravitational attraction. It was recently shown that without self-interaction super-critical boson stars are unstable to decay into their individual constituents. Here we show that this is no longer true for the self-interacting case and that boson stars can possess spatial oscillations in the scalar field. We also discuss the corresponding black hole solutions that carry charged scalar hair.

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关于超临界带电玻色子星的注释

我们研究带电玻色子星从亚临界状态到超临界状态的转变。这种转变被定义为耦合常数的选择，两个单独的玻色子（组成恒星）的库仑斥力恰好抵消了它们的引力。最近的研究表明，如果没有自相互作用，超临界玻色子星就不稳定，无法衰变成其单独的成分。在这里，我们证明这对于自相互作用的情况不再成立，并且玻色子星可以在标量场中拥有空间振荡。我们还讨论了相应的携带带电标量毛发的黑洞解决方案。