中心黑洞自引力玻色-爱因斯坦凝聚体的质量-半径关系
Mass-radius relation of self-gravitating Bose-Einstein condensates with a central black hole
摘要：
我们确定了具有由中心质量产生的吸引$-1/r$外势的自引力玻色-爱因斯坦凝聚体的质量-半径关系。根据我们以前的工作[P. H。Chavanis，Phys.Rev.D84，043531（2011）]，我们使用基于高斯分析的分析方法。我们考虑的情况下，非相互作用的玻色子以及自相互作用玻色子的情况下，排斥或吸引的自我相互作用。这些结果可能会在自引力玻色-爱因斯坦凝聚体形成的暗物质晕中找到应用。在这种情况下，中心质量可能会模仿一个超大质量黑洞。我们将我们的结果应用到超轻轴子与有吸引力的自相互作用。我们确定了中心黑洞如何影响质量半径关系和我们以前的论文中发现的轴子晕的最大质量。我们的近似分析结果的基础上的高斯分析结果进行了比较，在特定的限制下得到的精确的分析结果。
英文摘要：
We determine the mass-radius relation of self-gravitating Bose-Einstein condensates with an attractive $-1/r$ external potential created by a central mass. Following our previous work [P.H. Chavanis, Phys. Rev. D 84, 043531 (2011)], we use an analytical approach based on a Gaussian ansatz. We consider the case of noninteracting bosons as well as the case of self-interacting bosons with a repulsive or an attractive self-interaction. These results may find application in the context of dark matter halos made of self-gravitating Bose-Einstein condensates. In that case, the central mass may mimic a supermassive black hole. We apply our results to ultralight axions with an attractive self-interaction. We determine how the central black hole affects the mass-radius relation and the maximum mass of axionic halos found in our previous papers. Our approximate analytical results based on the Gaussian ansatz are compared with exact analytical results obtained in particular limits.
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