In this paper, we analyze trajectories of spacelike curves that are critical points of a Lagrangian depending on its total torsion. We focus on two important families of spacetimes, generalized Robertson–Walker and standard static spacetimes. For the former, we show that such trajectories are those with a constant curvature. For the latter, we also obtain a characterization in terms of the curvature of the trajectory but in this case measured with an appropriate conformal metric.

中文翻译：

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三维非真空时空中具有扭转的相对论粒子

在本文中，我们分析了空间曲线的轨迹，这些曲线是拉格朗日函数的关键点，取决于其总扭转。我们关注两个重要的时空族，广义罗伯逊-沃克时空和标准静态时空。对于前者，我们表明这些轨迹是具有恒定曲率的轨迹。对于后者，我们还获得了轨迹曲率的表征，但在这种情况下，使用适当的保形度量进行测量。