Quasinormal mode spectrum of a Kerr black hole in the eikonal limit
Quasinormal mode spectrum of a Kerr black hole in the eikonal limit
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DOI：
10.1103/physrevd.82.104003
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发表时间：
2010-07
影响因子：
5
通讯作者：
S. Dolan
中科院分区：
文献类型：
--
作者：
S. Dolan
众所周知，黑洞对一般扰动的响应是由被称为准正则模的衰减共振谱来表征的；并且，在大角动量极限(L和gt；>；1)中，准正则模的频谱与不稳定零轨道的性质有关。在本文中，我们开发了一种扩展方法来探索这种联系。我们得到了大L区轻阻尼谱部分的新的闭合形式近似。我们证实，在L的前导阶处，共振频率与相应零轨道的轨道频率有关，共振衰减与相应的零轨道的李亚普诺夫指数有关。我们比以往的研究走得更远，建立了(I)赤道(m={+-}L)模的1/L阶频率的自旋相关修正，以及(Ii)极化模(m=0)的一个新结果。我们通过测试闭合形式的近似与用Leaver方法数值获得的频率来验证该方法。
It is well established that the response of a black hole to a generic perturbation is characterized by a spectrum of damped resonances, called quasinormal modes; and that, in the limit of large angular momentum (l>>1), the quasinormal mode frequency spectrum is related to the properties of unstable null orbits. In this paper we develop an expansion method to explore the link. We obtain new closed-form approximations for the lightly damped part of the spectrum in the large-l regime. We confirm that, at leading order in l, the resonance frequency is linked to the orbital frequency, and the resonance damping to the Lyapunov exponent, of the relevant null orbit. We go somewhat further than previous studies to establish (i) a spin-dependent correction to the frequency at order 1/l for equatorial (m={+-}l) modes, and (ii) a new result for polar modes (m=0). We validate the approach by testing the closed-form approximations against frequencies obtained numerically with Leaver's method.