2024/08/06 by Pendás-Recondo, Enrique · 2 citations
#53C22 #53C60 #53C80 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2408.03206
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.