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(1) Is the gravitational singularity (or space-time singularity) the same as the black hole singularity?

(2) The wikipedia page says

Physicists are undecided whether the prediction of singularities means that they actually exist (or existed at the start of the Big Bang), or that current knowledge is insufficient to describe what happens at such extreme densities.

Is this really true? As I know, A lot of physicists think there is no real singularity in nature, but are they still unable to make decisions about the existence of actual singularities? I wonder if there is no singularity in nature apart from the completion of physics theory that can measure or predict a certain physical quantity by removing physical infinity.

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  • $\begingroup$ To exist means to move in time. The GR singularities don't move in time, so they don't exist. Counting time by Planck units $t_h$, the beginning of the universe is not $t=0$, but $t=t_h$, at which point $t\ne 0$, so the size is not zero either, thus no true singularity. In black holes, singularity does not exist for an external observer, because the internal spacetime is causally disconnected from ours. For an internal observer, the singularity does not exist at any moment of time until time ends. Again, the last moment is one Planck unit away from the end and then nothing. So no singularity. $\endgroup$
    – safesphere
    Commented Aug 26, 2018 at 5:21

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1) Yes. A physical singularity in General Relativity occurs when the Kretschmann scalar diverges.

2) General Relativity (GR) predicts the existence of black holes, and using GR in cosmology produces a prediction of the origin of the universe called the "Big Bang." Black holes and the Big Bang are both physical singularities, and we have lots of evidence to support the existence of these predictions. However, by definition a singularity means that you cannot "know" anything about where/when the singularity occurs. Thus, we have insufficient knowledge about these singular entities to be able to say what kind of being they are beyond what we get from GR. So, we need a theory that will subsume GR and that will explain more: precisely those singularities. This is an active field of research, and is one of the main motivations for a quantum theory of gravity.

Most physicists take the philosophical view that a physical singularity exists, just that the theory that describes it as a singularity is insufficient to describe what's "behind" the singularity (it's like an impassable mathematical wall caused by a division by zero).

Your distinction between "physical" and "actual" singularities is empty. Black holes exist! They are actual, physical entities, it's just that we need a better theory if we want to theorize testable predictions about what occurs beyond the event horizon of a black hole.

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  • $\begingroup$ "Yes. A physical singularity in General Relativity occurs when the Kretschmann scalar diverges." From what I remember, a singularity is defined using imcomplete geodesics. Wald discusses specifically why divergence of various curvature scalars including the Kretschmann scalar is not a good enough criterion upon which to define singularities in section 9.1 of his book "General Relativity". $\endgroup$
    – enumaris
    Commented Aug 23, 2018 at 16:40
  • $\begingroup$ The Kretschmann scalar is sufficient for most examples (i.e. Schw, Kerr BH's, and FRW spacetimes). But you are correct that a more sophisticated approach is the construction of geodesics that terminate - if such geodesics exist then they terminate at a singularity. The Kretschmann scalar is also conceptually nice because it is straight forward to calculate and shows the nature of the singularity's existence in a simple way. $\endgroup$
    – Daddy Kropotkin
    Commented Aug 23, 2018 at 22:05

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