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.
This remains true in this framework: setting only Λ = 0 we still find a solution provided T1 =T 2 =T 3 =T 4 = 0, f= 1− 2GM r ,(44)
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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.