A generalized lens equation for light deflection in weak gravitational fields

TL;DR

This paper introduces a new generalized lens equation for weak gravitational fields that accurately accounts for finite distances, bridging classical and post-Newtonian approaches, especially useful in extreme astrometrical scenarios.

Contribution

A novel generalized lens equation that incorporates finite source and observer distances, unifying classical and post-Newtonian light deflection models.

Findings

The generalized lens equation reduces to known models in appropriate limits.

Neglected terms are estimated to be within 15 Pi/4 (m/d')^2.

Applicable to extreme astrometrical configurations.

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.