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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?

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    $\begingroup$ 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". $\endgroup$
    – PM 2Ring
    Commented Apr 5, 2019 at 19:14
  • $\begingroup$ So can we say its equivalent to a blank space? $\endgroup$
    – TheVariant
    Commented Apr 5, 2019 at 19:20
  • $\begingroup$ 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. $\endgroup$
    – PM 2Ring
    Commented Apr 5, 2019 at 19:43
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    $\begingroup$ The function $\frac{1}{x^2}$ is continuous in all the points of the curve. But $x=0$ is not on the curve. $\endgroup$
    – peterh
    Commented Apr 5, 2019 at 19:45
  • $\begingroup$ @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. $\endgroup$
    – Chappo Hasn't Forgotten
    Commented Apr 5, 2019 at 23:12

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A singularity in physics is basically a big signpost saying "the theory you are using has probably ceased to be a good approximation of reality by the time you get here". An example is the infinite amount of short-wavelength radiation produced by a blackbody under the Rayleigh-Jeans law. This is obviously an incorrect description of reality and the issue ended up being resolved by the development of quantum theory: taking into account the corrections gives Planck's law, and the infinity goes away.

Inside a black hole, general relativity does predict singularities, and it seems to be fairly common to talk of them as though they are physical objects. However we should be cautious: even though general relativity is our best description of gravity so far, we already know that it does not describe the actual universe. The issue here is that general relativity is incompatible with the Standard Model of quantum field theory, which is our best theory of how physics works excluding gravity.

By the time you get to the region near where general relativity predicts a singularity, you're working with a very small region with an intense gravitational field. Quantum corrections are almost certainly going to be relevant here, and unfortunately we do not yet have a self-consistent theory of "quantum gravity" to describe what should happen in such a region and so far experiments (such as the ones being performed at the Large Hadron Collider) haven't given much of a clue as to how to proceed with developing one.

In a hypothetical universe where general relativity is correct then there would be a singularity (which is fortunately hidden from the rest of the universe by the event horizon), but we do not live in such a universe.

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