DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Phys Rev Lett. 2012 Feb 3;108(5):051104. doi: 10.1103/PhysRevLett.108.051104. Epub 2012 Jan 31.
We study the motion of a classical spinning particle (with spin degrees of freedom described by a vector of Grassmann variables) in higher-dimensional general rotating black hole spacetimes with a cosmological constant. In all dimensions n we exhibit n bosonic functionally independent integrals of spinning particle motion, corresponding to explicit and hidden symmetries generated from the principal conformal Killing-Yano tensor. Moreover, we demonstrate that in 4-, 5-, 6-, and 7-dimensional black hole spacetimes such integrals are in involution, proving the bosonic part of the motion integrable. We conjecture that the same conclusion remains valid in all higher dimensions. Our result generalizes the result of Page et al. [Phys. Rev. Lett. 98, 061102 (2007)] on complete integrability of geodesic motion in these spacetimes.
我们研究了带宇宙常数的高维广义转动黑洞时空中经典转动粒子（其转动自由度由一个格拉斯曼变量向量描述）的运动。在所有维度 n 中，我们展示了 n 个转动粒子运动的独立玻色积分，这些积分对应于由主共形 Killing-Yano 张量生成的显式和隐式对称性。此外，我们证明了在 4-、5-、6-和 7 维黑洞时空中，这些积分是对易的，从而证明了运动的玻色部分是可积的。我们推测，在所有更高维度中，同样的结论仍然成立。我们的结果推广了 Page 等人在这些时空中的测地线运动完全可积性的结果[Phys. Rev. Lett. 98, 061102 (2007)]。
