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Could someone please explain how we know the singularity has an infinite density and zero size/volume? From reading around online black holes have a defined radius (the event horizon) but this isn't its true size, it's just a reference point. If a supermassive star is so large that neuron degeneracy pressure cannot halt the collapse then it turns into a black hole. But I don't see how scientists know it has zero size? They say the mass is in a volume smaller than an electron but how do they know this? How do they know all the massive at the singularity isn't in some tiny (but finite) volume?

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  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/24934/2451 , physics.stackexchange.com/q/18981/2451 and links therein. $\endgroup$
    – Qmechanic
    Mar 19, 2023 at 18:14
  • $\begingroup$ @safesphere - I haven't sourced those statements about singularities from 'pop-pseudo' sources. en.wikipedia.org/wiki/Gravitational_singularity - second paragraph, first sentence '.......in the context of general relativity, where density would become infinte.......' Also, youtube.com/watch?v=fPtdJZyudd0 - 4mins 50s to 5mins 20s he says exactly what I said. This is a lecturer (retired) from MIT who dedicated his whole life to astrophysics. You really saying in that clip thats all false? $\endgroup$
    – user37250
    Mar 19, 2023 at 20:11
  • $\begingroup$ Thanks @safesphere. Yes I heard he was stripped of that. Sad as I used to think highly of him due his motivating lectures and all his great achievements are somewhat tainted now. Would you say this is a good enough quick summary of it: dailymotion.com/video/x621wmg if you go to 19mins 30s. He uses a bit of the actual tensor theory. $\endgroup$
    – user37250
    Mar 22, 2023 at 18:36
  • $\begingroup$ I mean I'll take your word it :D Thanks for the detailed response. So are you saying that whatever lies at the centre of the black hole GR is likely to be able to explain it? i.e. black holes do not cause GR to break down as most web links seem to say. Also, if a neutron star cannot withhold the collapse of a very large star, if not a singularity with zero size, it must collapse into something very small? If this is on the scale of quantum particles surely GR couldn't explain that? $\endgroup$
    – user37250
    Mar 25, 2023 at 0:01
  • $\begingroup$ This is interesting - youtube.com/watch?v=W39kfrxOSHg that guy does get roasted especially around the 33 minute mark. Interesting how roger penrose is not convinced with QM. $\endgroup$
    – user37250
    Mar 25, 2023 at 1:31

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The singularity arises as a solution from Einstein's field equations.However singularities in physics is a red flag that we push to its limit the theory which predicts the singularity.As closer as we get to the center of a black hole,the more quantum effects start to dominate.However we dont have a theory of quantum gravity to tell us what will happen there.And even if we did physics isnt math we need physical evidence to support a theory and since past the event horizon that part of the universe is forever inaccessible to us we may never confirm the truth.However in the future if we manage to create tiny black holes in particle accelerators and study these tiny black holes maybe we can have a very good guess on what is happening past the event horizon of a stellar or bigger black hole.

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Could someone please explain how we know the singularity has an infinite density and zero size/volume ?

We don't. We cannot observe anything beyond the event horizon. All we can say is that if the theory of general relativity continues to apply everywhere inside the event horizon then there will be a singularity at the centre of the black hole (this is a consequence of the Penrose-Hawking singularity theorems). However, a singularity appears to be a non-physical outcome. This is one of the reasons why physicists believe that general relativity must break down at some point inside a black hole - but we don't yet have a viable theory of quantum gravity to replace it.

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