标题： 比较可穿越虫洞周围粒子运动的自旋补充条件 显示英文标题

标题： Comparing spin supplementary conditions for particle motion around traversable wormholes

摘要： 运动的自旋测试粒子的运动由Mathisson-Papapetrou-Dixon（MPD）方程描述。众所周知，这些方程将黎曼曲率张量与反对称自旋张量S耦合，并结合四速度的归一化条件，是一个将十四个未知数联系起来的十一方程组。为了“闭合”该系统，有必要引入形式为V_\mu S^{\mu \nu } = 0的约束，通常称为自旋补充条件（SSC），其中V_\mu 是一个未来指向的参考向量，满足归一化条件V_\alpha V^\alpha = -1 。文献中存在几种SSC。特别是Tulzcyjew-Dixon、Mathisson-Pirani和Ohashi-Kyrian-Semerák是社区中最常用的。从物理观点来看，选择不同的SSC（不同的参考向量$V^\mu$）等同于固定测试粒子的质心。在本文中，我们比较了围绕Morris-Thorne可穿越虫洞运动的自旋测试粒子的不同SSC。为此，我们首先获得轨道频率，并将其展开到粒子自旋的三阶；正如预期的那样，零阶与开普勒频率一致，所有SSC中都相同；然而，我们发现展开的二阶中出现了差异，类似于施瓦茨希尔德和克尔黑洞。我们还比较了内稳定圆轨道（ISCO）的行为。由于每个SSC与测试粒子的不同质心相关，我们分别分析了每个SSC的径向和自旋修正。我们发现径向修正提高了收敛性，尤其是在Tulzcyjew-Dixon和Mathisson-Pirani SSC之间。在Ohashi-Kyrian-Semerák的情况下，我们发现自旋修正消除了ISCO的发散，并扩展了其对于粒子更高自旋值的存在性。 显示英文摘要

摘要： The Mathisson-Papapetrou-Dixon (MPD) equations describe the motion of spinning test particles. It is well-known that these equations, which couple the Riemann curvature tensor with the antisymmetric spin tensor S, together with the normalization condition for the four-velocity, is a system of eleven equations relating fourteen unknowns. To ``close'' the system, it is necessary to introduce a constraint of the form V_\mu S^{\mu \nu} = 0, usually known as the spin supplementary condition (SSC), where V_\mu is a future-oriented reference vector satisfying the normalization condition V_\alpha V^\alpha = -1. There are several SSCs in the literature. In particular, the Tulzcyjew-Dixon, Mathisson-Pirani, and Ohashi-Kyrian-Semer\'ak are the most used by the community. From the physical point of view, choosing a different SSC (a different reference vector $V^\mu$) is equivalent to fixing the centroid of the test particle. In this manuscript, we compare different SSCs for spinning test particles moving around a Morris-Thorne traversable wormhole. To do so, we first obtain the orbital frequency and expand it up to third-order in the particle's spin; as expected, the zero-order coincides with the Keplerian frequency, the same in all SSCs; nevertheless, we found that differences appear in the second order of the expansion, similar to the Schwarzschild and Kerr black holes. We also compare the behavior of the innermost stable circular orbit (ISCO). Since each SSC is associated with a different centroid of the test particle, we analyze (separately) the radial and spin corrections for each SSC. We found that the radial corrections improve the convergence, especially between Tulzcyjew-Dixon and Mathisson-Pirani SSCs. In the case of Ohashi-Kyrian-Semer\'ak, we found that the spin corrections remove the divergence for the ISCO and extend its existence for higher values of the particle's spin.