Wind Finslerian structures: from Zermelo's navigation to the causality of spacetimes
Wind Finslerian structures: from Zermelo's navigation to the causality of spacetimes
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风芬斯勒结构：从策梅洛的导航到时空的因果关系
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Miguel Sánchez Caja
中科院分区：
文献类型：
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作者：
E. Caponio;M. Javaloyes;Miguel Sánchez Caja
风Finsler结构的概念的发展，这是一个推广的Finsler度量的指标在切空间可能不包含零向量。在这些指标是椭圆体的特殊情况下，这里称为风黎曼结构，它们允许双重解释，提供：（a）经典Zermelo导航问题的模型，即使移动物体的轨迹（飞机，轮船）受到强风或急流的影响，和（B）一个自然的因果结构的相对论时空赋予一个非零的Killing向量场（SSTK分裂），在芬斯勒元素的描述。这些元素可以看作是部分柯西超曲面上的共形不变Killing初值。风Finsler结构中描述的两个（圆锥曲线，伪）Finsler度量，一个凸指标和其他凹的。然而，风黎曼情形的时空观点给出了一个有用的统一观点。对这样一个时空的因果性质的彻底研究是在芬斯勒条件下进行的。当Killing向量场是类时或类光时，Randers-Kropina度量出现为SSTK的Finslerian对应物。在应用程序中，我们得到的解决方案Zermelo的导航与任意固定风，度量型属性（距离型到达函数，完整性，存在的最小化，最大化或封闭测地线），以及描述的时空元素（柯西发展，黑洞视界）的芬斯勒元素在Killing初始数据。一个一般的费马原理的独立利益的任意时空，以及它的应用SSTK时空和策梅罗的导航，也提供了。
The notion of wind Finslerian structure is developed; this is a generalization of Finsler metrics where the indicatrices at the tangent spaces may not contain the zero vector. In the particular case that these indicatrices are ellipsoids, called here wind Riemannian structures, they admit a double interpretation which provides: (a) a model for classical Zermelo's navigation problem even when the trajectories of the moving objects (planes, ships) are influenced by strong winds or streams, and (b) a natural description of the causal structure of relativistic spacetimes endowed with a non-vanishing Killing vector field (SSTK splittings), in terms of Finslerian elements. These elements can be regarded as conformally invariant Killing initial data on a partial Cauchy hypersurface. The wind Finslerian structure is described in terms of two (conic, pseudo) Finsler metrics, one with a convex indicatrix and the other with a concave one. However, the spacetime viewpoint for the wind Riemannian case gives a useful unified viewpoint. A thorough study of the causal properties of such a spacetime is carried out in Finslerian terms. Randers-Kropina metrics appear as the Finslerian counterpart to the case of an SSTK when the Killing vector field is either timelike or lightlike. Among the applications, we obtain the solution of Zermelo's navigation with arbitrary stationary wind, metric-type properties (distance-type arrival function, completeness, existence of minimizing, maximizing or closed geodesics), as well as description of spacetime elements (Cauchy developments, black hole horizons) in terms of Finslerian elements in Killing initial data. A general Fermat's principle of independent interest for arbitrary spacetimes, as well as its applications to SSTK spacetimes and Zermelo's navigation, are also provided.
黎曼几何和芬斯勒几何中的一些紧性定理
DOI：
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发表时间：
2018
期刊：
影响因子：
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作者：
足立真訓;Jihun Yum;Pozar Norbert;Homare TADANO
通讯作者：
Homare TADANO