16 Pages, 18 figures, An invited short review and accepted for publication in Commun. Theor. Phys. Some minor error in the original version are corrected
We give a brief review on the formation and the calculation of black hole shadow. Firstly, we introduce the conception of black hole shadow and the current works on a variety of black hole shadows. Secondly, we present main methods of calculating photon sphere radius and shadow radius, and then explain how the photon sphere affect the boundary of black hole shadow. We review the analytical calculation for black hole shadows which have analytic expressions for shadow boundary due to the integrable photon motion system. And we introduce the fundamental photon orbits which can explain the patterns of black hole shadow shape. Finally, we review the numerical calculation of black hole shadows with the backward ray-tracing method, and introduce some chaotic black hole shadows with self-similar fractal structures. Since the gravitational waves from the merger of binary black holes have been detected, we introduce a couple of shadows of binary black holes, which all have the eyebrowlike shadows around the main shadows with the fractal structures. We discuss the invariant phase space structures of photon motion system in black hole space-time, and explain the formation of black hole shadow is dominated by the invariant manifolds of certain Lyapunov orbits near the fixed points.
Geometrothermodynamics of Black Hole Shadows: A Review
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Dipartimento di Fisica and ICRA, Università di Roma “La Sapienza”（罗马第一大学物理系及ICRA）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）
Probing Quantum Gravity through Chaotic Orbits and Strong-Field Effects in Kerr Black Holes Embedded in Perfect Fluid Dark Matter
The Institute of Mathematical Sciences, C.I.T. Campus（泰米鲁纳德邦金奈塔拉马尼 CIT 校区的数学科学研究所）；Khazar University（阿塞拜疆巴库的哈萨尔大学）；University of Mazandaran（伊朗巴巴萨尔的马赞达兰大学）；Virtual University of Pakistan（巴基斯坦拉合尔的虚拟大学）；Hemwati Nandan Bahuguna Garhwal University（印度北阿坎德邦斯里纳加的赫姆瓦蒂·南丹·巴胡加纳加尔瓦尔大学）；Harbin Institute of Technology（中国哈尔滨的哈尔滨工业大学）；Zhejiang Normal University（中国金华的浙江师范大学）
Distorting Kerr Images with Parity-Odd Scalar Hair
South China University of Technology（华南理工大学）；Shanghai Jiao-Tong University（上海交通大学）；University of Jinan（济南大学）；Beijing Normal University（北京师范大学）；School of Physical Science and Technology, Ningbo University（宁波大学物理科学与技术学院）；Peking University（北京大学）
