Numerical treatment of the light propagation problem in the post-Newtonian formalism

TL;DR

This paper presents a numerical approach to study the evolution of light wavefronts in a post-Newtonian spacetime, analyzing their curvature and effects on arrival times using ray tracing and surface fitting techniques.

Contribution

It introduces a numerical method combining ray tracing and surface fitting to analyze light wavefront curvature in a relativistic framework.

Findings

Wavefront curvature relates to changes in arrival times.

Numerical methods effectively model light propagation in post-Newtonian spacetime.

Surface fitting accurately determines wavefront curvature.

Abstract

The geometry of a light wavefront, evolving from a initial flat wavefront in the 3-space associated with a post-Newtonian relativistic spacetime, is studied numerically by means of the ray tracing method. For a discretization of the bidimensional light wavefront, a surface fitting technique is used to determine the curvature of this surface. The relationship between the intrinsic curvature of the wavefront and the change of the arrival time at different points on the Earth is also numerically discussed.