I Space like hypersurface

Apashanka

If two events are occuring in a space like hypersurface....is it that the two events will appear to be simultaneous from a frame moving with velocity $v\lt c$ and will appear to be occuring at the same spatially position from a frame with velocity $v\gt c$??

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Ibix

If two events are occuring in a space like hypersurface....is it that the two events will appear to be simultaneous from a frame moving with velocity $v\lt c$
In flat spacetime, yes. In curved spacetime there are no global frames, and you have to be a bit more careful with your definition. It would be better to say something like that they lie in a plane whose tangent vectors are everywhere spacelike.
a frame with velocity $v\gt c$??
You cannot consistently describe such a thing.

Orodruin

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Clarification: The events will be simultaneous in some frame. They will not be simultaneous in all frames.

"Space like hypersurface"

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