# 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?

• As Ben Crowell says on the Physics site: "A singularity in GR is like a piece that has been cut out of the manifold. It's not a point or point-set at all". – PM 2Ring Apr 5 '19 at 19:14
• So can we say its equivalent to a blank space? – sk9298 Apr 5 '19 at 19:20
• It's worse than that. To keep things simple, imagine that we only have 2 dimensions, 1 of time & 1 of space, so we can draw a map on paper of the spacetime containing a black hole. Where the singularity is, it's not merely blank paper, there's actually a hole in the paper. – PM 2Ring Apr 5 '19 at 19:43
• The function $\frac{1}{x^2}$ is continuous in all the points of the curve. But $x=0$ is not on the curve. – peterh - Reinstate Monica Apr 5 '19 at 19:45
• @peterh excellent example! Correct if just looking at points on the two curves, but the function is actually discontinuous over the domain $\mathbb {R}$, which of course is the point you're illustrating. – Chappo Hasn't Forgotten Monica Apr 5 '19 at 23:12