We consider the problem of quantum field theory on the Bertotti-Robinson space-time, which arises naturally as the near horizon geometry of an extremal Reissner-Nordstrom black hole but can also arise in certain near-horizon limits of non-extremal Reissner Nordstrom space-time. The various vacuum states have been considered in the context of $AdS_{2}$ black holes by Spradlin and Strominger who showed that the Poincare vacuum, the Global vacuum and the Hartle-Hawking vacuum are all equivalent, while the Boulware vacuum and the Schwarzschild vacuum are equivalent. We verify this by explicitly computing the Green's functions in closed form for a massless scalar field corresponding to each of these vacua. Obtaining a closed form for the Green's function corresponding to the Boulware vacuum is non-trivial, we present it here for the first time by deriving a new summation formula for associated Legendre functions that allows us to perform the mode-sum. Having obtained the propagator for the Boulware vacuum, which is a zero-temperature Green's function, we can then consider the case of a scalar field at an arbitrary temperature by an infinite image imaginary-time sum, which yields the Hartle-Hawking propagator upon setting the temperature to the Hawking temperature. Finally, we compute the renormalized stress-energy tensor for a massless scalar field in the various quantum vacua.
From Bertotti--Robinson to Vacuum: New Exact Solutions in General Relativity via Harrison and Inversion Symmetries
Institute of Mathematics of the Czech Academy of Sciences（捷克科学院数学研究所）；Vicerrectoría de Investigación y Postgrado, Universidad de La Serena（拉塞雷纳大学研究与研究生院）；Sede Esmeralda, Universidad de Tarapacá（塔帕卡里大学埃斯梅尔达校区）；Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院理论物理研究所）；Departamento de Física, Universidad de Concepción（康塞普西翁大学物理系）
Ultrarelativistic boost of a black hole in the magnetic universe of Levi-Civita--Bertotti--Robinson
Institute of Mathematics of the Czech Academy of Sciences（捷克科学院数学研究所）；Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile（智利南方大学物理与数学科学研究所）；Departamento de Ciencias, Facultad de Artes Liberales, UAI Physics Center, Universidad Adolfo Ibañez（阿道夫·伊巴涅斯大学自由艺术学院科学系、UAI物理中心）
Thermodynamics of Kerr-Newman-Bertotti-Robinson black holes
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研究所、物理科学与技术学院）；School of Physics, & Center for High Energy Physics, Peking University（北京大学物理学院、高能物理中心）
University of Science and Technology of China（中国科学技术大学）；Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院）；Peng Huanwu Center for Fundamental Theory（彭桓武理论物理中心）；Ningbo University（宁波大学）
Light bending around the Kerr-Bertotti-Robinson black hole using material medium approach
National Institute of Technology, Agartala（阿加塔拉国家技术学院）；The Institute of Mathematical Sciences（数学科学研究所）；Khazar University（汗扎尔大学）；Hemwati Nandan Bahuguna Garhwal University（赫姆瓦蒂·南丹·巴胡加纳加尔瓦尔大学）；Centre for Space Research, North-West University（西北大学空间研究中心）；Assam University（阿萨姆大学）
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）
Optical and thermodynamic properties of Kerr-Bertotti-Robinson black holes
California State University, Fresno（弗雷斯诺加州州立大学）；University of Hradec Králové（赫拉德茨克拉洛韦大学）；Khazar University（卡扎尔大学）；Nazarbayev University（纳扎尔巴耶夫大学）；National Taiwan University（台湾大学）；Arizona State University（亚利桑那州立大学）；University of Helsinki（赫尔辛基大学）；Università di Camerino（卡梅里诺大学）；University at Albany-SUNY（奥尔巴尼纽约州立大学）；INAF - Osservatorio Astronomico di Brera（意大利国家天体物理研究所-布雷拉天文台）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Center for Theoretical Physics, Khazar University（卡扎尔大学理论物理中心）
Chaotic motion and power spectral density in Schwarzschild Bertotti-Robinson black hole spacetime
Harbin Institute of Technology（哈尔滨工业大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高级研究院）；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）；Institute of Fundamental and Applied Research, National Research University TIIAME（TIIAME国立研究型大学基础与应用研究所）；Tashkent State Technical University（塔什干国立技术大学）
Thermodynamics of Kerr-Bertotti-Robinson black hole
University of Chinese Academy of Sciences (UCAS)（中国科学院大学）；Hangzhou Institute for Advanced Study (HIAS), University of Chinese Academy of Sciences (UCAS)（中国科学院大学杭州高等研究院）；Institute of Theoretical Physics, Chinese Academy of Sciences (CAS)（中国科学院理论物理研究所）；Ningbo University（宁波大学）；Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心）
Dynamics, Ringdown, and Accretion-Driven Multiple Quasi-Periodic Oscillations of Kerr-Bertotti-Robinson Black Holes
Zhejiang Normal University（浙江师范大学）；American University of the Middle East（中东美国大学）；Madhabdev University（马哈德夫大学）；Khazar University（阿塞拜疆可萨大学）；Jamia Millia Islamia（贾米亚米利亚伊斯兰大学）；University of KwaZulu-Natal（夸祖鲁-纳塔尔大学）；National University of Sciences and Technology（国立科学与技术大学）；Harbin Institute of Technology（哈尔滨工业大学）
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）
Gravitational wave signatures from periodic orbits around a Schwarzschild-Bertotti-Robinson black hole
National Research University TIIAME（国立TIIAME大学）；Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；United Center for Gravitational Wave Physics (UCGWP), Zhejiang University of Technology（浙江工业大学引力波物理联合中心）
Global structure and stability of Kerr-Bertotti-Robinson spacetime
University of Science and Technology of China（中国科学技术大学）；Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院）；Peng Huanwu Center for Fundamental Theory（彭桓武理论物理中心）；Ningbo University（宁波大学）
