On the application of Lorentz-Finsler geometry to model wave propagation

TL;DR

This paper reviews how Lorentz-Finsler geometry can be used to model wave propagation in anisotropic, time-dependent media by representing wave paths as lightlike pregeodesics of a specific Lorentz-Finsler metric, enabling real-time computation.

Contribution

It provides a clear, step-by-step methodology for constructing and implementing Lorentz-Finsler models for wave propagation in complex media.

Findings

Wave trajectories are modeled as lightlike pregeodesics.

The Lorentz-Finsler model obeys Fermat's and Huygens' principles.

The resulting ODE system is computationally efficient for real-time applications.

Abstract

The recent increasing interest in the study of Lorentz-Finsler geometry has led to several applications to model real-world physical phenomena. Our purpose is to provide a simple, step-by-step review on how to build and implement such a geometric model to describe the propagation of a classical wave satisfying Fermat's and Huygens' principles in an anisotropic and rheonomic (time-dependent) medium. The model is based on identifying the individual wave trajectories as lightlike pregeodesics of a specific Lorentz-Finsler metric, which obey a simple ODE system and can therefore be easily computed in real time.