2020/09/08 by Tadashi Sasaki, Hisao Suzuki
Physics and Astronomy · #Astrophysical Phenomena and Observations #Bending #Black Holes and Theoretical Physics #Black hole (networking) #Deflection (physics) #General relativity #Gravitation #Pulsars and Gravitational Waves Research #Schwarzschild metric #Schwarzschild radius #Series (stratigraphy) #Spacetime #gr-qc #hep-th
paper · pdf · doi:10.1088/1361-6382/ac0456
10 pages, 2 figures
arxiv created 2020/09/08 · openalex created_date 2020/09/14 · openalex publication_date 2021/05/24 · arxiv updated 2021/07/07 · openalex updated_date 2026/08/05
Abstract The bending of light rays by gravitational sources is one of the first evidence of general relativity. When the gravitational source is a stationary massive object such as a black hole, the bending angle has an integral representation, from which various series expansions up to a finite order in terms of the parameters of orbit and the background spacetime has been derived. However, it has not been clear that it has any analytic expansion. In this paper, we show that such an analytic expansion can be obtained for the case of a Schwarzschild black hole by solving an inhomogeneous Picard–Fuchs equation, which has been applied to compute effective superpotentials on D-branes in the Calabi–Yau manifolds. From the analytic expression of the bending angle, the full order expansions in both weak and strong deflection limits are obtained. We show that the result can be obtained by the direct integration approach as well. We also discuss how the charge of the gravitational source affects the bending angle and show that a similar analytic expression can be obtained for the extremal Reissner–Nordström spacetime.