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Discontinuity in space-time

What I understood about it till now is that space-time fabric is kind of broken there. Please tell me whether I am correct.

  • If it's true then does it mean that perception of time will stop there?

  • I really can't get what broken space fabric is like. If it's a hole then how is matter supposed to be present inside that?

  • Is a black hole a discontinuity?