Huygens' envelope principle in Finsler spaces and analogue gravity

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.

17 pages, 3 figures. Final version accepted for publication in CQG. Animations in Supplementary Material available at http://vigo.ime.unicamp.br/Huygens/

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• Measurement of stimulated Hawking emission in an analogue system
• Observation of negative-frequency waves in a water tank: A classical analogue to the Hawking effect?
• Planck-scale modified dispersion relations and Finsler geometry
• Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
• Detecting Rotational Superradiance in Fluid Laboratories
• The geometry of sound rays in a wind

Cited by in corpus (4)

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• Wind-Finslerian structure of black holes
• An account on links between Finsler and Lorentz Geometries for Riemannian Geometers