高贵的引力原子：具有角动量数的自引力黑洞标量场
Noble gravitational atoms: Self-gravitating black hole scalar wigs with angular momentum number
AI总结：
本文提出了一种新的球对称解，描述了围绕黑洞的自引力标量场配置，包括角动量数ℓ。通过类比于ℓ-玻色星的方法，构建了自引力的'引力原子'，并将其称为'高贵的引力原子'。研究显示，这些原子在事件视界附近与ℓ-玻色星有显著差异，其大小、密度和寿命因参数而异。
摘要：
我们提出了Einstein-Klein-Gordon方程在准稳态近似下的新球对称解，描述了围绕黑洞的自引力标量场配置，包括角动量数ℓ。采用类比于生成ℓ-玻色星的方法，构建了自引力的'引力原子'，其中ℓ≥0。我们将这些新解称为'高贵的引力原子'，类比于具有闭合电子壳层的 noble atoms。我们证明，在适当极限下，高贵的引力原子全球上接近ℓ-玻色星，仅在事件视界附近有显著差异。具有ℓ>0的引力原子有时在相对较远处有密度最大值，对于ℓ>1，其近邻密度较小。此外，当ℓ>0时，它们不总是表现出典型的事件视界密度尖峰；相反，有时会表现出小的凹陷。当ℓ=0时，尖峰可能出现，但其对总质量密度的贡献总是可以忽略不计。这些物体的大小、密度和寿命因参数而异，有时可以达到银河系的规模，密度可以稀疏到暗物质的程度，寿命可以长到宇宙本身。
英文摘要：
We present new spherically symmetric solutions of the Einstein-Klein-Gordon equations in a quasi-stationary approximation that describe self-gravitating scalar field configurations around a black hole, including angular momentum number $\ell$. An approach analogous to the one which gives rise to $\ell$-boson stars is used here to construct self-gravitating ``gravitational atoms" with $\ell\ge0$. We refer to these new solutions as {\it noble gravitational atoms}, by analogy with noble atoms, which are characterized by closed electron shells. We show that, in the proper limit, noble gravitational atoms approach $\ell$-boson stars globally, displaying noticeable differences only in a region very close to the event horizon. Noble gravitational atoms with $\ell>0$ sometimes present density maxima located at relatively large radii, with small density close to the horizon for $\ell>1$. Furthermore, they do not always present the typical density spike at the event horizon if $\ell > 0$; on the contrary, they sometimes exhibit a small dip there. When $\ell=0$, a spike can appear, but its contribution to the total mass density is always negligible. The size, density, and lifetime of these objects vary significantly depending on the parameters, being in some cases as large as galaxies, as dilute as dark matter, and as long-lived as the Universe itself.
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