A1 Refereed original research article in a scientific journal
Accurate analytic formula for light bending in Schwarzschild metric
Authors: Juri Poutanen
Publisher: EDP SCIENCES S A
Publication year: 2020
Journal: Astronomy and Astrophysics
Journal name in source: ASTRONOMY & ASTROPHYSICS
Journal acronym: ASTRON ASTROPHYS
Article number: ARTN A24
Volume: 640
Number of pages: 7
ISSN: 0004-6361
DOI: https://doi.org/10.1051/0004-6361/202037471
Web address : https://doi.org/10.1051/0004-6361/202037471
Self-archived copy’s web address: https://arxiv.org/abs/1909.05732
Abstract
We propose new analytic formulae describing light bending in the Schwarzschild metric. For an emission radii above the photon orbit at the 1.5 Schwarzschild radius, the formulae have an accuracy of better than 0.2% for the bending angle and 3% for the lensing factor for any trajectories that turn around a compact object by less than about 160 degrees. In principle, they can be applied to any emission point above the horizon of the black hole. The proposed approximation can be useful for problems involving emission from neutron stars and accretion discs around compact objects when fast accurate calculations of light bending are required. It can also be used to test the codes that compute light bending using exact expressions via elliptical integrals.
We propose new analytic formulae describing light bending in the Schwarzschild metric. For an emission radii above the photon orbit at the 1.5 Schwarzschild radius, the formulae have an accuracy of better than 0.2% for the bending angle and 3% for the lensing factor for any trajectories that turn around a compact object by less than about 160 degrees. In principle, they can be applied to any emission point above the horizon of the black hole. The proposed approximation can be useful for problems involving emission from neutron stars and accretion discs around compact objects when fast accurate calculations of light bending are required. It can also be used to test the codes that compute light bending using exact expressions via elliptical integrals.
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