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

http://arxiv.org/abs/1604.08308


We discuss a possible extension of calculations of the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime to a non-asymptotically 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 non-asymptotically flat spacetimes to suggest finite-distance corrections: Schwarzschild-de Sitter (Kottler) solution to the Einstein equation and an exact solution in Weyl conformal gravity.

Read this paper on arXiv…

A. Ishihara, Y. Suzuki, T. Ono, et. al.
Fri, 13 May 16
37/63

Comments: 22 pages, 4 figures