Perturbations of slowly rotating black holes: massive vector fields in the Kerr metric
Perturbations of slowly rotating black holes: massive vector fields in the Kerr metric
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DOI：
10.1103/physrevd.86.104017
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发表时间：
2012-09
影响因子：
5
通讯作者：
P. Pani;V. Cardoso;L. Gualtieri;E. Berti;A. Ishibashi
中科院分区：
文献类型：
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作者：
P. Pani;V. Cardoso;L. Gualtieri;E. Berti;A. Ishibashi
我们讨论了一种研究缓慢旋转黑洞的线性扰动的通用方法，该方法对于任何扰动场都有效，并且当场方程不可分离时特别有利。作为该方法的说明，我们研究了 Kerr 度量中的大量矢量（Proca）扰动，这在标准 Teukolsky 形式主义中似乎是不可分离的。在微扰方案中，我们讨论了旋转引起的两个重要效应：非轴对称准正规模式和具有不同方位角数 m 的束缚态的塞曼式位移，以及具有不同多极指数 l 的轴向模式和极性模式之间的耦合。我们明确计算旋转中高达二阶的扰动方程，但原则上该方法可以扩展到任何阶。在旋转的一阶工作中，我们表明可以通过求解两组解耦方程组来计算极坐标和轴向 Proca 模式，并且我们导出了一个描述自旋 s=0 和 s=+-1 的轴向扰动的单个主方程。通过将计算扩展到二阶，我们可以以自洽的方式研究普罗卡扰动的超辐射状态。我们首次证明克尔黑洞周围的普罗卡场表现出超辐射不稳定性，这种不稳定性明显强于大质量标量场。由于这种不稳定性，旋转黑洞的天体物理观测提供了光子质量的最严格上限：在我们最保守的假设下，mv<4x10^-20 eV。对最大黑洞的自旋测量可以将这一界限降低到 mv<10^-22 eV 或更低。
We discuss a general method to study linear perturbations of slowly rotating black holes which is valid for any perturbation field, and particularly advantageous when the field equations are not separable. As an illustration of the method we investigate massive vector (Proca) perturbations in the Kerr metric, which do not appear to be separable in the standard Teukolsky formalism. Working in a perturbative scheme, we discuss two important effects induced by rotation: a Zeeman-like shift of nonaxisymmetric quasinormal modes and bound states with different azimuthal number m, and the coupling between axial and polar modes with different multipolar index l. We explicitly compute the perturbation equations up to second order in rotation, but in principle the method can be extended to any order. Working at first order in rotation we show that polar and axial Proca modes can be computed by solving two decoupled sets of equations, and we derive a single master equation describing axial perturbations of spin s=0 and s=+-1. By extending the calculation to second order we can study the superradiant regime of Proca perturbations in a self-consistent way. For the first time we show that Proca fields around Kerr black holes exhibit a superradiant instability, which is significantly stronger than for massive scalar fields. Because of this instability, astrophysical observations of spinning black holes provide the tightest upper limit on the mass of the photon: mv<4x10^-20 eV under our most conservative assumptions. Spin measurements for the largest black holes could reduce this bound to mv<10^-22 eV or lower.