标题： 芬斯勒空间中的惠更斯包络原理与类比引力 显示英文标题

标题： Huygens' envelope principle in Finsler spaces and analogue gravity

摘要： 我们将最近一个关于芬斯勒空间中波前有效性的惠更斯包络原理的定理推广到$n$维的情形。我们的结果直接应用于类引力模型，其中费马最小时间原理自然产生一个潜在的芬斯勒几何结构。为了说明这一点，我们考虑了两个由近期实验结果启发的具体例子：水槽中的表面波和涡流。对于这两个例子，我们都发现了独特的方向时空结构，即视界和能层。我们证明这两种结构都与潜在的芬斯勒（Randers）几何中的某些方向发散有关。我们的结果表明芬斯勒几何可能为时空的因果结构提供一个新的视角，不仅适用于类比模型，也适用于广义相对论。 显示英文摘要

摘要： 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.