# Huygens' envelope principle in Finsler spaces and analogue gravity

## TL;DR

This paper generalizes Huygens' envelope principle to Finsler spaces and explores its implications in analogue gravity, demonstrating how Finsler geometry can elucidate causal structures like horizons and ergospheres.

## Contribution

It extends a recent theorem to n-dimensional Finsler spaces and applies it to analogue gravity models, linking wavefront behavior to Finslerian geometric structures.

## Key findings

- Huygens' principle holds in n-dimensional Finsler spaces.
- Finsler geometry reveals directional divergences related to horizons and ergospheres.
- Applications to surface waves and vortices demonstrate the geometric approach.

## Abstract

We extend to the $n$-dimensional case a recent theorem establishing the validity of the Huygens' envelope principle for wavefronts in Finsler spaces. Our results have direct applications in analogue gravity models, for which the Fermat's principle of least time naturally gives origin to an underlying Finslerian geometry. For the sake of illustration, we consider two explicit examples motivated by recent experimental results: surface waves in flumes and vortices. For both examples, we have distinctive directional spacetime structures, namely horizons and ergospheres, respectively. We show that both structures are associated with certain directional divergences in the underlying Finslerian (Randers) geometry. Our results show that Finsler geometry may provide a fresh view on the causal structure of spacetime, not only in analogue models but also for General Relativity.