标题： 质量标量场在Kerr黑洞时空中的准束缚态：超越氢原子近似 显示英文标题

标题： Quasi-bound states of massive scalar fields in the Kerr black-hole spacetime: Beyond the hydrogenic approximation

摘要： 旋转的黑洞在其外部区域可以支持质量标量场的准稳态（不稳定的）束缚态共振。 这些空间上规则的标量构型的特点是不稳定性时间尺度远长于由中心黑洞的几何尺寸（质量）设定的时间尺度$M$。 众所周知，在小质量极限$\alpha\equiv M\mu\ll1$（这里$\mu$是标量场的质量）下，这些准稳态标量共振的特点是熟悉的氢原子振荡谱：$\omega_{\text{R}}/\mu=1-\alpha^2/2{\bar n}^2_0$，其中整数$\bar n_0(l,n;\alpha\to0)=l+n+1$是束缚态共振的主量子数（在这里整数$l=1,2,3,...$和$n=0,1,2,...$分别是球面谐波指数和场模的共振参数）。 由于它仅依赖于主共振参数$\bar n_0$，这个小质量（$\alpha\ll1$）类氢光谱显然是简并的。 在本文中，我们超越了小质量近似，并分析了在快速旋转的克尔黑洞时空中的大质量标量场的准稳态束缚态共振，在该区域$\alpha=O(1)$。 特别是，我们推导出了非类氢（并且一般来说是非简并的）共振振荡光谱${{\omega_{\text{R}}}/{\mu}}=\sqrt{1-(\alpha/{\bar n})^2}$，其中$\bar n(l,n;\alpha)=\sqrt{(l+1/2)^2-2m\alpha+2\alpha^2}+1/2+n$是准稳态共振的广义主量子数。 该用于组合黑洞-大质量标量场系统的特征振荡频率的解析公式被证明与准稳态束缚态共振的直接数值计算结果一致。 显示英文摘要

摘要： Rotating black holes can support quasi-stationary (unstable) bound-state resonances of massive scalar fields in their exterior regions. These spatially regular scalar configurations are characterized by instability timescales which are much longer than the timescale $M$ set by the geometric size (mass) of the central black hole. It is well-known that, in the small-mass limit $\alpha\equiv M\mu\ll1$ (here $\mu$ is the mass of the scalar field), these quasi-stationary scalar resonances are characterized by the familiar hydrogenic oscillation spectrum: $\omega_{\text{R}}/\mu=1-\alpha^2/2{\bar n}^2_0$, where the integer $\bar n_0(l,n;\alpha\to0)=l+n+1$ is the principal quantum number of the bound-state resonance (here the integers $l=1,2,3,...$ and $n=0,1,2,...$ are the spheroidal harmonic index and the resonance parameter of the field mode, respectively). As it depends only on the principal resonance parameter $\bar n_0$, this small-mass ($\alpha\ll1$) hydrogenic spectrum is obviously degenerate. In this paper we go beyond the small-mass approximation and analyze the quasi-stationary bound-state resonances of massive scalar fields in rapidly-spinning Kerr black-hole spacetimes in the regime $\alpha=O(1)$. In particular, we derive the non-hydrogenic (and, in general, non-degenerate) resonance oscillation spectrum ${{\omega_{\text{R}}}/{\mu}}=\sqrt{1-(\alpha/{\bar n})^2}$, where $\bar n(l,n;\alpha)=\sqrt{(l+1/2)^2-2m\alpha+2\alpha^2}+1/2+n$ is the generalized principal quantum number of the quasi-stationary resonances. This analytically derived formula for the characteristic oscillation frequencies of the composed black-hole-massive-scalar-field system is shown to agree with direct numerical computations of the quasi-stationary bound-state resonances.