A Fermat principle for stationary space-times and applications to light rays |
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| Institution: | 1. Dipartimento di Matematica, Università di Bari, Bari, Italy;2. Istituto di Matematiche Applicate, Università di Pisa, Pisa, Italy;3. Dipartimento di Matematica, Politecnico di Bari, Bari, Italy;1. School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China;2. School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China;1. Shaanxi Key Laboratory of Space Solar Power Station System, Xidian University, Xi’an 710071, China;2. Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, China;3. Key Laboratory of Electronic Equipment Structure Design of Ministry of Education, Xidian University, Xi’an 710071, China;1. School of Science, Xi''an University of Architecture and Technology, Xi’an, China;2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, China;3. National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, Suzhou, China |
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| Abstract: | We present an extension of the classical Fermat principle in optics to stationary space-times. This principle is applied to study the light rays joining an event with a timelike curve. Existence and multiplicity results of light rays are proved. Moreover, Morse Relations relating the set of rays to the topology of the space-time are obtained, by using the number of conjugate points of the ray. The results hold also for stationary space-times with boundary, in particular the Kerr space-time outside the stationary limit surface. |
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