# Does General Relativity require that Spacetime must be a orientable? [duplicate]

Possible Duplicate:
Can spacetime be non-orientable?

Apart from the constraints put on the topology of spacetime by QFT (Parity For example), if the global topology of a universe is that of a Mobius band and at one point there is a gravitational field pointing towards a star and a passenger travels along the band and returns to the same point. Then he will find the gravitational field pointing away from the star causing an anti-gravity effect. Does this mean that space-time must be orientable?

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