Finite-distance corrections to the gravitational bending angle of light in the strong deflection limit

TL;DR

This paper develops a method using the Gauss-Bonnet theorem to accurately calculate finite-distance corrections to the gravitational bending angle of light in strong deflection scenarios, with potential observational relevance.

Contribution

It introduces a novel approach to include finite-distance effects in gravitational lensing calculations using the Gauss-Bonnet theorem, applicable in strong deflection limits.

Findings

Finite-distance corrections can be as large as 10^{-5} arcseconds for Sgr A*.

Corrections for the Sun in the weak field are also around 10^{-5} arcseconds.

The method may improve the precision of future astronomical observations.

Abstract

Continuing work initiated in an earlier publication [Ishihara, Suzuki, Ono, Kitamura, Asada, Phys. Rev. D {\bf 94}, 084015 (2016) ], we discuss a method of calculating the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime, especially by taking account of the finite distance from a lens object to a light source and a receiver. For this purpose, we use the Gauss-Bonnet theorem to define the bending angle of light, such that the definition can be valid also in the strong deflection limit. Finally, this method is applied to Schwarzschild spacetime in order to discuss also possible observational implications. The proposed corrections for Sgr A$^{\ast}$ for instance are able to amount to $\sim 10^{-5}$ arcseconds for some parameter range, which may be within the capability of near-future astronomy, while also the correction for the Sun in the weak field limit is $\sim 10^{-5}$ arcseconds.