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We extend to the $n$-dimensional case a recent theorem establishing thevalidity of the Huygens' envelope principle for wavefronts in Finsler spaces.Our results have direct applications in analogue gravity models, for which theFermat's principle of least time naturally gives origin to an underlyingFinslerian geometry. For the sake of illustration, we consider two explicitexamples motivated by recent experimental results: surface waves in flumes andvortices. For both examples, we have distinctive directional spacetimestructures, namely horizons and ergospheres, respectively. We show that bothstructures are associated with certain directional divergences in theunderlying Finslerian (Randers) geometry. Our results show that Finslergeometry may provide a fresh view on the causal structure of spacetime, notonly in analogue models but also for General Relativity.

Huygens' envelope principle in Finsler spaces and analogue gravity