Gravitational bending angle of light for finite distance and the Gauss-Bonnet theorem

2016/04/30 by Asahi Ishihara, Yusuke Suzuki, Toshiaki Ono +2 · 285 citations
Mathematics · Physics and Astronomy · #Adaptive optics and wavefront sensing #Bending #Classical mechanics #Gauss #Gauss–Bonnet theorem #Geometry #Gravitation #History and Developments in Astronomy #Mathematics #Physics #Quantum mechanics #Relativity and Gravitational Theory #astro-ph.CO #gr-qc

paper · pdf · doi:10.1103/physrevd.94.084015

published in Physical review. D/Physical review. D. 94(8) (American Physical Society) · 22 pages, 5 figures, accepted by PRD

arxiv created 2016/09/29 · openalex publication_date 2016/10/10 · arxiv updated 2016/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We discuss a possible extension of calculations of the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime to a nonasymptotically flat case. We examine a relation between the bending angle of light and the Gauss-Bonnet theorem by using the optical metric. A correspondence between the deflection angle of light and the surface integral of the Gaussian curvature may allow us to take account of the finite distance from a lens object to a light source and a receiver. Using this relation, we propose a method for calculating the bending angle of light for such cases. Finally, this method is applied to two examples of the nonasymptotically flat spacetimes to suggest finite-distance corrections: the Kottler (Schwarzschild--de Sitter) solution to the Einstein equation and an exact solution in Weyl conformal gravity.

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