Autoparallel motion in a class of torsionful Schwarzschild spacetimes is completely integrable via four conserved quantities, and positive-energy autoparallels are repelled by the black hole.
Integrability Conditions for Killing-Yano Tensors and Maximally Symmetric Spaces in the Presence of Torsion
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abstract
The integrability conditions for the existence of Killing-Yano tensors or, equivalently, covariantly closed conformal Killing-Yano tensors, in the presence of torsion are worked out. As an application, all metrics and torsions compatible with the existence of a Killing-Yano tensor of order n-1 are obtained. Finally, the issue of defining a maximally symmetric space with respect to connections with torsion is addressed.
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`Translation invariant' black hole: autoparallels and complete integrability
Autoparallel motion in a class of torsionful Schwarzschild spacetimes is completely integrable via four conserved quantities, and positive-energy autoparallels are repelled by the black hole.