A generalized lens equation for light deflection in weak gravitational fields

Abstract

A generalized lens equation for weak gravitational fields in Schwarzschild metric and valid for finite distances of source and observer from the light deflecting body is suggested. The magnitude of neglected terms in the generalized lens equation is estimated to be smaller than or equal to 15 Pi/4 (m/d')^2, where m is the Schwarzschild radius of massive body and d' is Chandrasekhar's impact parameter. The main applications of this generalized lens equation are extreme astrometrical configurations, where 'Standard post-Newtonian approach' as well as 'Classical lens equation' cannot be applied. It is shown that in the appropriate limits the proposed lens equation yields the known post-Newtonian terms, 'enhanced' post-post-Newtonian terms and the Classical lens equation, thus provides a link between these both essential approaches for determining the light deflection.

11 pages, 3 figures

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• Studying Gravitational Deflection of Light by Kiselev Black Hole via Homotopy Perturbation Method
• Time transfer functions in Schwarzschild-like metrics in the weak-field limit: A unified description of Shapiro and lensing effects
• Light propagation in 2PN approximation in the field of one moving monopole II. Boundary value problem
• Modelling the Sgr A${}^{\ast }$ and M87${}^{\ast }$ shadows by using the Kerr-Taub-NUT metrics in the presence of a scalar field
• Light deflection in binary stars