Raychaudhuri Equation and Weyl-Driven Shear: A Weak-Field Approach to Lensing and Gravitational Waves

TL;DR

This paper investigates gravitational lensing and wave propagation in the weak-field regime using the Raychaudhuri equation, emphasizing the critical role of shear and Weyl curvature in these phenomena.

Contribution

It introduces a novel application of the Raychaudhuri equation for shear in weak-field gravitational phenomena, highlighting the significance of Weyl curvature in lensing and gravitational waves.

Findings

Shear plays a crucial role in gravitational lensing and wave propagation.

Weyl curvature tensor significantly influences lensing and gravitational wave behavior.

A damped harmonic oscillator model effectively describes Weyl effects in these phenomena.

Abstract

The letter studies phenomena like gravitational wave propagation and gravitational lensing using the celebrated Raychaudhuri equation (RE) in the weak field limit. Newtonian analogue of Relativistic RE has been explored. In doing so, role of shear has been found to be extremely important in explaining these phenomena. Consequently, the RE for shear has been used in course of the study and importance of Weyl curvature tensor in lensing and gravity wave propagation has been explicitly shown using a damped harmonic oscillator approach.