# Does spacetime could curved in a square way ?

Does spacetime could curved in a "square way"?

Suppose there is a square mass object in the universe (I know its impossible, but suppose...).
Does spacetime will curved in a "square way"?
I believe that not as GR is defined on a smooth manifold.
Am I right?

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HallsofIvy
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Suppose there is a square mass object in the universe (I know its impossible, but suppose...).
Does spacetime will curved in a "square way"?
I believe that not as GR is defined on a smooth manifold.
Am I right?
When you start off by postulating an impossible situation there is no point in asking what GR would say- it would say "that is impossible"!

What exactly is impossible about a square mass object?

You mean a massive cube, right? Or a very flat square pancake? In any case, you can apply GR to any shape of object, the distortion of space-time at a distance will be about the same as for a spherical object, but closer by the curvature will be influenced by the shape. Nothing stops you from simply integrating over the volume, I don't see the problem.

Of course a real object can't be perfectly square, since atoms are sort of round, but even if it was, any measurement of space-time curvature would be at some non-zero distance from the object, so everything already starts smoothing out a bit, and there will be no discontinuities. Is that the answer you were looking for?

Yes, this is the answer I have been looking for.
Thanks a lot!!!