On Integrability of spinning particle motion in higher-dimensional black hole spacetimes

Details On Integrability of spinning particle motion in higher-dimensional black hole spacetimes On Integrability of spinning particle motion in higher-dimensional black hole spacetimes

2011-10-03

arxiv.org/abs/1110.0495v2

Phys. Rev. Lett. 108, 051104 (2012)

Physics

High Energy Physics

High Energy Physics - Theory

Version 2: revised version, added references. 5 pages, no figures

Scientific paper

10.1103/PhysRevLett.108.051104

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. [hep-th/0611083] on complete integrability of geodesic motion in these spacetimes.

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