The spectra of gravitational atoms
The spectra of gravitational atoms
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DOI：
10.1088/1475-7516/2019/12/006
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发表时间：
2019-12-01
影响因子：
6.4
通讯作者：
ter Haar, Lotte
中科院分区：
文献类型：
--
作者：
Baumann, Daniel;Chia, Horng Sheng;ter Haar, Lotte
计算了旋转黑洞周围超轻标量场和矢量场的准束缚态谱。这些光谱由引力精细结构常数α决定，α是黑洞的大小与场的康普顿波长的比值。当α较小时，能量本征值和不稳定率可以解析计算。由于解在黑洞视界附近迅速变化，普通的微扰近似法失效，我们必须使用匹配的渐近展开法来确定谱。我们的分析处理依赖于运动方程的可分性，因此只适用于标量场和矢量场的电模式。然而，对于缓慢旋转的黑洞，磁模式的方程可以写成可分离的形式，我们利用它来推导它们的能量本征值，并推测它们的不稳定率的解析形式。为了检验我们的猜想，并将所有结果扩展到大的α值，我们数值求解光谱。我们解释了如何准确和有效地计算这些光谱，而不依赖于可分性。这使我们能够获得可靠的结果，任何α大于或接近0.001和黑洞的任意自旋。我们的研究结果提供了一个必不可少的输入黑洞周围的玻色子云的现象学，特别是当这些是二进制系统的一部分。
We compute the quasi-bound state spectra of ultralight scalar and vector fields around rotating black holes. These spectra are determined by the gravitational fine structure constant alpha, which is the ratio of the size of the black hole to the Compton wavelength of the field. When alpha is small, the energy eigenvalues and instability rates can be computed analytically. Since the solutions vary rapidly near the black hole horizon, ordinary perturbative approximations fail and we must use matched asymptotic expansions to determine the spectra. Our analytical treatment relies on the separability of the equations of motion, and is therefore only applicable to the scalar field and the electric modes of the vector field. However, for slowly-rotating black holes, the equations for the magnetic modes can be written in a separable form, which we exploit to derive their energy eigenvalues and conjecture an analytic form for their instability rates. To check our conjecture, and to extend all results to large values of alpha, we solve for the spectra numerically. We explain how to accurately and efficiently compute these spectra, without relying on separability. This allows us to obtain reliable results for any alpha greater than or similar to 0.001 and black holes of arbitrary spin. Our results provide an essential input to the phenomenology of boson clouds around black holes, especially when these are part of binary systems.