玻色-爱因斯坦凝聚超大质量黑洞：弯曲时空中重整化量子场论的一个例子
Bose-Einstein condensed supermassive black holes: a case of renormalized quantum field theory in curved space-time
摘要：
本文研究了一个现实的黑洞是否可以在原则上类似于一颗恒星，在它的视界有一个大的但有限的红移。如果物质散布在质量为$M\sim10^9M_\odot$的超大质量黑洞的内部，它的平均密度与空气相当，它可能是由密集的氢原子组成的玻色-爱因斯坦凝聚体产生的。在具有正宇宙学常数的相对论引力理论中，描述H原子的玻色子量子场与曲率标量之间存在无量纲耦合$ξ$。在玻色-爱因斯坦凝聚基态中，当$ξ$为黑洞质量的二次函数时，度规的精确自洽解出现。提出了通过适当选择背景度规作为重正化方法的第一步来设置$ξ$，否则非线性很小。这个黑洞有一根头发，即结合能。考虑了基态的涨落。
英文摘要：
This paper investigates the question whether a realistic black hole can be in principal similar to a star, having a large but finite redshift at its horizon. If matter spreads throughout the interior of a supermassive black hole with mass $M\sim10^9M_\odot$, it has an average density comparable to air and it may arise from a Bose-Einstein condensate of densely packed H-atoms. Within the Relativistic Theory of Gravitation with a positive cosmological constant, a bosonic quantum field describing H atoms is coupled to the curvature scalar with dimensionless coupling $ξ$. In the Bose-Einstein condensed groundstate an exact, self-consistent solution for the metric occurs for a certain large value of $ξ$, quadratic in the black hole mass. It is put forward that $ξ$ is set by proper choice of the background metric as a first step of a renormalization approach, while otherwise the non-linearities are small. The black hole has a hair, the binding energy. Fluctuations about the ground state are considered.
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