# How is spacetime curved?

How about multi-verse?
How about gravity leaking into and out of this universe?
How about quantum gravity? String theory? Loop gravity?

A plane, a mobius strip, and a cylinder are all equivalent locally - any small neighborhood can be smoothly mapped into R^2.

All of the above are even flat - you can make any of them out of a flat sheet of paper with no problems.

But they aren't equivalent globally.
That is of course true. Now by reading the above mentioned quote again I realize I misread it.

The above mentioned flat geometries are obviously semi-Riemannian as well, initially I read it in a contrasting way as if those flat geometries were not semi-Riemannian.
Sorry, my mistake!

thank you for this explanation, this has been messing with me for a few weeks.

Lets say that i just place a ball on the curved sheet without gravity - it will just sit there when really it should be rolling to the middle. This is a resualt of the fact that the analogy fails to show how the passage through time causes the ball to acually roll towards the center. In the equator analogy this is easily shown if you look at the "north" direction as time and the longitude as space - then even if two bodies are placed on opposite sides of the equator since they're constantly moving "north" through time they will eventually meet at a pole.