Dark matter density can be significantly enhanced by the supermassive black hole at the galactic center, leading to a structure called dark matter spike. Dark matter spike may change the spacetime properties of black holes that constitute deviations from GR black holes. Based on these interesting background, we construct a set of solutions of black holes in a dark matter spike under the Newtonian approximation and full relativity. Combining the mass model of M87, we study the quasinormal modes of black holes in the scalar field and axial gravitational perturbation, then compared them with Schwarzschild black hole. Besides, the impacts of dark matter on the quasinormal mode of black holes have been studied in depth. In particular, in the axial gravitational perturbation, our results show that the impacts of dark matter spike on the quasinormal mode of black holes can reach up to $10^{-4}$. These new features from quasinormal mode of black holes under the Newtonian approximation and full relativity may provide some help for the establishment of the final dark matter model, and provide a new thought for the indirect detection of dark matter.
Probing Bardeen-Kiselev black hole with cosmological constant caused by Einstein equations coupled with nonlinear electrodynamics using quasinormal modes and greybody bounds
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）
Proper-Time Approach in Asymptotic Safety via Black Hole Quasinormal Modes and Grey-body Factors
University of Hradec Kralove（赫拉德茨克拉洛韦大学）；Istanbul University（伊斯坦布尔大学）；National Research University TIIAME（塔什干国立技术大学TIIAME）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）；Urgench State University（乌尔根奇国立大学）；Kimyo International University in Tashkent（塔什干基莫国际大学）；Mamun University（马蒙大学）
Constraint on environments with eccentric extreme-mass-ratio inspirals: Bayesian inference and Fisher-matrix for dark-matter spikes
College of Computer and Big data, Putian University（莆田学院计算机与大数据学院）；Nanchang University（南昌大学）；Center for Relativistic Astrophysics and High Energy Physics, Nanchang University（南昌大学相对论天体物理与高能物理中心）
Scalar quasinormal modes of rotating black holes in parity-violating gravity
Tokyo Metropolitan University（东京都立大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；College of Humanities and Sciences, Nihon University（日本大学文理学部）；Chulalongkorn University（朱拉隆功大学）；The University of Tokyo（东京大学）
Quasinormal modes of scalar perturbations in Rastall thick brane
School of Mathematics and Physics, Jingchu University of Technology（荆楚理工学院数学与物理学院）；Center for Fundamental Physics, School of Mechanics and Photoelectric Physics, Anhui University of Science and Technology（安徽理工大学力学与光电物理学院基础物理中心）
Probing higher curvature gravity via ringdown with overtones
Kaichi Tokorozawa Secondary School（东京都立小平高等学校）；Department of Physics, Rikkyo University（立教大学物理系）；Department of Information, Artificial Intelligence and Data Science, Daiichi Institute of Technology（第一工业大学信息、人工智能与数据科学系）；Department of Physics, Tokyo Metropolitan University（东京都立大学物理系）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Department of Physics, College of Humanities and Sciences, Nihon University（日本大学人文学部物理系）
研究高曲率引力中黑洞的度规扰动，发现高曲率修正使有效势近邻区域变形，泛音模式的 quasinormal mode 频率偏离 GR 值更显著，分析高曲率引力模型中的回波波形。
Echoes of a hairy black hole from gravitational decoupling
Guizhou University of Finance and Economics（贵州财经大学）；Eastern Mediterranean University（东地中海大学）；Universit degli Studi di Salerno（萨莱诺大学）；Istituto Nazionale di Fisica Nucleare - Gruppo Collegato di Salerno - Sezione di Napoli（意大利国家核物理研究所 - 萨莱诺协作组 - 那不勒斯分部）；Guizhou Minzu University（贵州民族大学）；Guizhou University（贵州大学）
Waveform stability of black hole ringdown with stochastic horizon structure
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础物理与数学科学学院）
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）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础物理与数学学院）；Escola de Engenharia de Lorena, Universidade de São Paulo（圣保罗大学洛雷纳工程学院）
