Accurate analytic formula for light bending in Schwarzschild metric

Abstract

We propose new analytic formulae describing light bending in Schwarzschild metric. For emission radii above the photon orbit at 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 deg. 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.

7 pages, 8 figures, submitted to A&A

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• Propagation of light in the presence of gravity generated by static and spherically symmetric curved space-times using Maxwell equations
• Intensity and Polarization Characteristics of Extended Neutron Star Surface Regions
• Effects of scattering in the accretion funnel on the pulse profiles of accreting millisecond pulsars
• Fundamental physics with neutron stars
• Two-blackbody portraits of radiation from magnetized neutron stars
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• Constraints on the $\gamma$-parameter for the vacuum solution of Cotton gravity with geodesics and shadows
• Pulsed, Polarized X-ray Emission from Neutron Star Surfaces: the Effects of Vacuum Birefringence in the Magnetosphere
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