Geodesics around the five-dimensional BPS one-brane are smooth and open for positive coupling q, while negative q creates a repulsive singular sphere that splits the spacetime into disconnected regions.
On Integrability of spinning particle motion in higher-dimensional black hole spacetimes
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abstract
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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The geodesic structure of BPS one-branes in five dimensions
Geodesics around the five-dimensional BPS one-brane are smooth and open for positive coupling q, while negative q creates a repulsive singular sphere that splits the spacetime into disconnected regions.