We discuss an approach to obtaining black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second order ordinary differential equations. We introduce the standard version of this method and present an improvement more suitable for numerical implementation. We demonstrate that the AIM can be used to find radial QNMs for Schwarzschild, Reissner-Nordstrom (RN) and Kerr black holes in a unified way. An advantage of the AIM over the standard continued fraction method (CFM) is that for differential equations with more than three regular singular points Gaussian eliminations are not required. However, the convergence of the AIM depends on the location of the radial or angular position, choosing the best such position in general remains an open problem. This review presents for the first time the spin 0, 1/2 & 2 QNMs of a Kerr black hole and the gravitational and electromagnetic QNMs of the RN black hole calculated via the AIM, and confirms results previously obtained using the CFM. We also presents some new results comparing the AIM to the WKB method. Finally we emphasize that the AIM is well suited to higher dimensional generalizations and we give an example of doubly rotating black holes.
Black hole quasinormal modes using the asymptotic iteration method
在这篇文章中，我们表明，渐近迭代方法（AIM）允许一个数值上找到Schwarzschild和Schwarzschild de Sitter（SdS）黑洞的准正规模式。该方法的另一个好处是，它也可以用来计算自旋为零扰动情况下的史瓦西反德西特（SAdS）准正规模。我们还讨论了一个改进的版本的AIM，更适合于数值实现。
Quasinormal modes of black holes in Weyl gravity: Electromagnetic and gravitational perturbations
最近报道的引力波探测激发人们研究不同黑洞模型的性质，特别是它们在（轴向）引力扰动下的行为。本文研究了外尔引力场中黑洞的拟正规模。利用Schwarzschild-anti de Sitter黑洞与Weyl解的关系，以及Weyl作用量的共形不变性，导出了描述拟正规辐射的主方程.由于度规函数中存在一个额外的线性$r$项，Weyl解的拟正规模谱偏离Schwarzschild黑洞的拟正规模谱.我们还考虑了背景时空中麦克斯韦场的演化，得到了电磁扰动的主方程。然后，我们使用WKB近似和渐近迭代方法来计算拟正规频率。最后，通过对主方程的时域积分，研究了模式的时间演化。
Asymptotic quasinormal modes, echoes, and black hole spectral instability: a brief review
Zhejiang Guangsha Vocational and Technical University of Construction（浙江广厦建设职业技术大学）；Turon University（图伦大学）；Faculdade de Engenharia de Guaratinguetá, Universidade Estadual Paulista（圣保罗州立大学瓜拉廷盖塔工程学院）；Natural Sciences Department, Metropolitan State University（大都会州立大学自然科学系）；Le Moyne College（莱莫恩学院）；Mathematics and Statistics Department, Metropolitan State University（大都会州立大学数学与统计系）；Escola de Engenharia de Lorena, Universidade de São Paulo（圣保罗大学洛雷纳工程学院）；Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University（扬州大学物理科学与技术学院引力与宇宙学中心）
Phase transitions and quasinormal modes of Euler-Heisenberg-dilaton AdS black holes
Jiangxi Normal University（江西师范大学）；Xihang University（西安大学）；Hunan Normal University（湖南师范大学）；Shaanxi University of Science and Technology（陕西科技大学）；Yangzhou University（扬州大学）
Quasinormal modes and greybody factors of magnetically charged de Sitter black holes probed by massless external fields in Einstein Euler Heisenberg gravity
Xihang University（西航大学）；National Joint Engineering Research Center for Special Pump System Technology, Xihang University（西航大学特种泵系统技术国家联合工程研究中心）；Yangzhou University（扬州大学）；Jiangxi Normal University（江西师范大学）
Charged scalar perturbations on charged black holes in dRGT massive gravity
研究了dRGT大质量引力场中一类带电黑洞中大质量带电标量场的准定态分布。我们讨论了度规中的线性项是dRGT质量引力的一个独特性质，它是如何影响时空结构的。对dRGT黑洞背景中带电标量场的准正规模进行了数值计算。对于渐近de Sitter（dS）黑洞，利用改进的渐近迭代法得到了相应的拟正规频率.对于$\ell=0$情形，发现了不稳定模，其实部满足超辐射条件。对于$\ell=2$，结果表明，所有的de Sitter黑洞在小扰动下都是稳定的.对于渐近dRGT anti de Sitter（AdS）黑洞，发现了频率满足超辐射条件的不稳定模.讨论了质量重力参数的影响。解析计算揭示了具有线性项的质量引力模型中准正规模的独特扩散性质。数值结果证实了在dS和AdS的情况下存在的特征扩散模式。
Superradiance and Quasinormal Modes of Massive Scalar Fields around Kerr Black Holes in Einstein-Maxwell-Dilaton-Axion Theory with Perfect Fluid Dark Matter
Division of Physical Science, Faculty of Science, Prince of Songkla University（宋卡王子大学理学院物理科学系）
Perturbations and quasinormal modes of black holes in general relativity coupled to nonlinear electrodynamics
School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高级研究所）；School of Electrical Engineering and Computer Science, National University of Sciences and Technology（国立科技大学电气与计算机工程学院）；Research Center of Astrophysics and Cosmology, Khazar University（哈扎尔大学天体物理学与宇宙学研究中心）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）
