The Kerr metric that describes the spacetime of a spinning supermassive black hole (SMBH) is axisymmetric, implying that the nearly parabolic geodesics on which stars approach the SMBH depend on the inclination angle $ι$ of the orbital angular momentum with respect to the SMBH spin. This inclination affects both the geodesic deviation that determines whether a star is tidally disrupted and whether the tidal debris survives direct capture by the event horizon to produce an observable tidal disruption event (TDE). The steady-state TDE rate is the rate at which stars are scattered into the loss cone determined by these spin- and inclination-dependent effects. As the anisotropy of this loss-cone refilling is highly uncertain, we consider the two extreme limits in which stellar inclination is preserved (IP) or isotropized (ISO). We calculate the inclination distribution in these two limits and find a prograde bias in the IP limit because of the strong retrograde bias for direct capture. However, we find a retrograde bias in the ISO limit for intermediate SMBH masses when the empty loss cone suppresses capture and allows the weaker retrograde bias of geodesic deviation to dominate. Partially empty loss cones lead to steeper distributions of the penetration factor $β$ than for a full loss cone, with this effect even more pronounced in the ISO limit. We also calculate the total TDE rates and maximum SMBH mass $M_{\rm \bullet, max}$ for tidal disruption in these two limits. In the IP limit, we find a highly spin-dependent capture cutoff in the TDE rate and $M_{\rm \bullet, max} \approx 10^{8.45} M_\odot$ for maximal SMBH spin. In the ISO limit, we find a strong spin-dependent enhancement in the TDE rate at intermediate SMBH masses, a weakly spin-dependent capture cutoff above $M_\bullet \approx 10^{7.5} M_\odot$, and $M_{\rm \bullet, max} \approx 10^{7.95} M_\odot$ for maximal SMBH spin.
Determining Kerr black hole spin and inclination from a segment of the critical curve in black hole images
Research and Education Center for Comprehensive Science, Akita Prefectural University（秋田县立大学综合科学教育与研究中心）；Department of Physics, Rikkyo University（立教大学物理系）
EMRIs in Kerr Spacetime: The Role of Inclination Diffusion
Racah Institute of Physics, The Hebrew University（拉卡物理研究所，希伯来大学）；Department of Astronomy, University of Wisconsin, Madison（威斯康星大学麦迪逊分校天文学系）；Department of Physics and MIT Kavli Institute, MIT（麻省理工学院物理系及MIT卡弗里研究所，麻省理工学院）
General relativistic hydrodynamics of stellar tidal disruptions in Kerr spacetime: methods, validation, and first applications
Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Hamburger Sternwarte, Universität Hamburg（汉堡天文台，汉堡大学）；The Oskar Klein Centre, Department of Astronomy, AlbaNova, Stockholm University（奥斯卡·克莱因中心，阿尔巴诺瓦，斯德哥尔摩大学天文学系）
Geodesics and Shadows in the Kerr-Bertotti-Robinson Black Hole Spacetime
Beijing Normal University（北京师范大学）；Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）；Tsung-Dao Lee Institute, Shanghai Jiao-Tong University（上海交通大学汤川研究所）；Institute of Fundamental Physics and Quantum Technology, & School of Physical Science and Technology, Ningbo University（宁波大学基础物理与量子技术学院、物理科学与技术学院）；School of Physics, Peking University, & Center for High Energy Physics（北京大学物理学院、高能物理中心）
Relativistic Thermal Emission from Accretion Disks in Kerr-MOG Spacetimes
Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大汤川研究所）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Key Laboratory for Particle Astrophysics and Cosmology (MOE) and Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University（粒子天体物理宇宙学教育部重点实验室和上海市粒子物理与宇宙学重点实验室，上海交通大学）；Institut für Theoretische Physik, Goethe-Universität Frankfurt（法兰克福歌德大学理论物理研究所）；Institute for Theoretical Physics & Cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）
Quantifying the impact of relativistic precession on tidal disruption event light curves
Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学与物理学院理论物理研究所）；Department of Physics and Columbia Astrophysics Laboratory, Columbia University（哥伦比亚大学物理学系与哥伦比亚天体物理实验室）；Center for Computational Astrophysics, Flatiron Institute（平顿研究所计算天体物理中心）；Department of Physics and Astronomy, Purdue University（普渡大学物理与天文系）；Hamburger Sternwarte, Universität Hamburg（汉堡大学汉堡天文台）；The Oskar Klein Centre, Department of Astronomy, AlbaNova, Stockholm University（斯德哥尔摩大学阿尔巴诺瓦天体物理奥斯卡·克莱因中心）
Critical Behavior of Photon Rings in Kerr-Bertotti-Robinson Spacetime
Institute of Fundamental Physics and Quantum Technology, and School of Physical Science and Technology, Ningbo University（宁波大学基础物理与量子技术研究所，物理科学与技术学院）；Tsung-Dao Lee Institute, Shanghai Jiao-Tong University（上海交通大学李政道研究所）；School of Physics, and Center for High Energy Physics, Peking University（北京大学物理学院，高能物理中心）
Autocorrelation in black hole flare movies: Departures from Kerr
Institute of Fundamental Physics and Quantum Technology, and School of Physical Science and Technology, Ningbo University（宁波大学基础物理与量子技术研究所和物理科学与技术学院）；Zhejiang Key Laboratory of Extreme Universe, and BINGO Center, Ningbo University（宁波大学浙江极端宇宙重点实验室和BINGO中心）；School of Physics, and Center for High Energy Physics, Peking University（北京大学物理学院和高能物理研究中心）
A fully relativistic twisted disk around a slowly rotating Kerr black hole: derivation of dynamical equations and the shape of stationary configurations
