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arXiv 2212.02530gr-qcastro-ph.COhep-ph
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半经典引力中的玻色子星及其近亲

Boson stars and their relatives in semiclassical gravity

Miguel Alcubierre, Juan Barranco, Argelia Bernal, Juan Carlos Degollado, Alberto Diez-Tejedor, Miguel Megevand, Darío Núñez, Olivier Sarbach

备注：
21 pages, 1 figure, 3 tables. To appear in Phys. Rev. D
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摘要：

在半经典引力近似下，我们构造了量子场论中的玻色子星组态。将我们的注意力限制在静态的情况下，我们证明了对于一个{ \it单实量子}标量场的半经典Einstein-Klein-Gordon系统，其状态描述了$N$ { \it全同粒子}的激发，每个粒子对应于一个给定的能级，可以约化为对于$N$ { \it复经典}标量场的Einstein-Klein-Gordon系统。特别考虑到球对称静态的情况下，能级标记的量子数$n$，$\ell$和$m$。当所有的粒子都处于基态$n=\ell=m=0$时，我们就得到了标准的静态玻色子星解，如果是$n\neq 0$，它就能被激发。另一方面，对于所有粒子都具有固定的径向和总角动量数$n$和$\ell$，其中有$\ell\neq 0$，但相对于它们的磁数$m$均匀分布的情况，人们得到$\ell$ -玻色子星，而当$\ell=m=0$和$n$取多个值时，得到多态玻色子星解。进一步推广了这些组态，包括多$\ell$多态玻色子星，它们构成了$N$ -粒子、静态、球对称、半经典实Einstein-Klein-Gordon系统的最一般解，其中粒子总数是确定的.尽管在多场经典理论中也会出现相同的时空结构，但在半经典引力中，它们是作为描述多体系统的单场状态的量子涨落而自然出现的。我们的研究结果可能对超轻标量场/模糊暗物质候选者的直接探测实验产生潜在影响。

英文摘要：

We construct boson star configurations in quantum field theory using the semiclassical gravity approximation. Restricting our attention to the static case, we show that the semiclassical Einstein-Klein-Gordon system for a {\it single real quantum} scalar field whose state describes the excitation of $N$ {\it identical particles}, each one corresponding to a given energy level, can be reduced to the Einstein-Klein-Gordon system for $N$ {\it complex classical} scalar fields. Particular consideration is given to the spherically symmetric static scenario, where energy levels are labeled by quantum numbers $n$, $\ell$ and $m$. When all particles are accommodated in the ground state $n=\ell=m=0$, one recovers the standard static boson star solutions, that can be excited if $n\neq 0$. On the other hand, for the case where all particles have fixed radial and total angular momentum numbers $n$ and $\ell$, with $\ell\neq 0$, but are homogeneously distributed with respect to their magnetic number $m$, one obtains the $\ell$-boson stars, whereas when $\ell=m=0$ and $n$ takes multiple values, the multi-state boson star solutions are obtained. Further generalizations of these configurations are presented, including the multi-$\ell$ multi-state boson stars, that constitute the most general solutions to the $N$-particle, static, spherically symmetric, semiclassical real Einstein-Klein-Gordon system, in which the total number of particles is definite. In spite of the fact that the same spacetime configurations also appear in multi-field classical theories, in semiclassical gravity they arise naturally as the quantum fluctuations associated with the state of a single field describing a many-body system. Our results could have potential impact on direct detection experiments in the context of ultralight scalar field/fuzzy dark matter candidates.

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