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.
Affine Killing vector fields on homogeneous surfaces with torsion
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abstract
Many extensions of General Relativity are based on considering metric and affine structures as independent properties of spacetime. This leads to the possibility of introducing torsion as an independent degree of freedom. In this article we examine the effects of torsion on the affine Killing vectors of two-dimensional manifolds. We give a complete description of the Lie algebras of affine Killing vector fields on homogeneous surfaces. This can be used in the search of non-metrizable surfaces of interest.
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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.