论文标题
Reissner-Nordström黑洞，支持非最小耦合的大规模标量现场配置
Reissner-Nordström black holes supporting non-minimally coupled massive scalar field configurations
论文作者
论文摘要
最近已经证明，可以在黑孔时段的外部区域支持静态的常规标量磁场，该静态常规标量磁场可在带电中央黑洞的电磁场上耦合。在本文中，我们使用{\ it分析}技术来研究无需大的大质量$μr_+\ gg1 $（在这里$ _+$ _++$ sallius saluded saluds and scalor scalor salive scalon的范围，在无尺寸的大质量级别$μr_+\ gg1 $中，在无尺寸的大型质量级别$μr_+\ gg1 $ y+\ gg1 $ y+\ gg1 $ gg1 $ y+\ gg1中的物理和数学特性以及 洞）。特别是，我们为离散的共振光谱$ \ \ {α_n（μ; q/m）\} _ {n = 0}^{n = \ infty} $得出了一个非常紧凑的分析公式，该公式表征了无量纲的黑色 - 毫米 - 毫米级构造的无限型参数。这种谐振光谱的物理意义源于以下事实：对于给定无量纲的黑洞电荷$ q/m $的给定值，基本的（最小）特征值$α_0（μ）$ $ $α_0（μ）决定了构成的黑洞 - 甲基机场系统的关键生存线，这使得非元素的毛线刺激了 - 刺激性的毛茸茸的毛茸茸的毛茸茸的毛茸茸的高度毛皮，并将其分离出来。秃头雷森纳德斯特斯特姆黑洞的配置。本文得出的分析结果通过直接数值计算证实。
It has recently been demonstrated that static spatially regular scalar fields, which are non-minimally coupled to the electromagnetic field of a charged central black hole, can be supported in the exterior regions of the black-hole spacetime. In the present paper we use {\it analytical} techniques in order to study the physical and mathematical properties of the externally supported linearized scalar field configurations (scalar 'clouds') in the dimensionless large-mass regime $μr_+\gg1$ (here $μ$ and $r_+$ are respectively the proper mass of the supported scalar field and the outer horizon radius of the central supporting black hole). In particular, we derive a remarkably compact analytical formula for the discrete resonant spectrum $\{α_n(μ;Q/M)\}_{n=0}^{n=\infty}$ which characterizes the dimensionless coupling parameter of the composed black-hole-non-minimally-coupled-linearized-massive-scalar-field configurations. The physical significance of this resonant spectrum stems from the fact that, for a given value of the dimensionless black-hole electric charge $Q/M$, the fundamental (smallest) eigenvalue $α_0(μ)$ determines the critical existence-line of the composed black-hole-massive-field system, a boundary line which separates non-linearly coupled hairy charged-black-hole-massive-scalar-field configurations from bald Reissner-Nordström black holes. The analytical results derived in this paper are confirmed by direct numerical computations.
