Does infinite curvature of spacetime really exist in physical world?
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3$\begingroup$ At which point do you think general relativity claims spacetime to be "infinitely curved" (note that the "point" at the center of a Schwarzschild black hole is called a "singularity" for a reason)? $\endgroup$– ACuriousMind ♦Commented Nov 29, 2016 at 22:53
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1$\begingroup$ Possible duplicate of Can we get infinite energy from space time (maybe curving it infinitely)? $\endgroup$– user108787Commented Nov 30, 2016 at 0:04
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Can space time really be infinitely curved (e.g by a black hole)?
A black hole doesn't curve spacetime, a black hole is (a region of) highly curved spacetime with, according to General Relativity (GR), a curvature singularity enclosed by an event horizon.
However, GR is a classical theory and, as far as we know, the physical world is better modeled with quantum theory. A quantum theory of gravity is still a work in progress.
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1$\begingroup$ This is Groundhog day, over and over, the same theme. physics.stackexchange.com/q/295469 $\endgroup$– user108787Commented Nov 29, 2016 at 23:53