2016/10/10 by Asahi Ishihara, Yusuke Suzuki, Toshiaki Ono +2 · 12 citations
Physics and Astronomy · #Relativity and Gravitational Theory #History and Developments in Astronomy #Adaptive optics and wavefront sensing
paper · doi:10.1103/physrevd.94.084015
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.