I hope the topic of this post is not too philosophical to be appropriate here.(adsbygoogle = window.adsbygoogle || []).push({});

Some recent discussions on PF have helped to crystallize my view of how classical GR treats singularities, and black hole singularities in particular. However, I'm not sure to what extent these ideas generalize to singularities that are not black hole singularities.

Singularities are not geometrical objects, in the sense that we can't even define basic geometrical properties for them such as how many dimensions they have: https://www.physicsforums.com/threads/boundary-construction-for-of-b-h-and-b-b-singularities.833399/ . "There is no there there."

Black hole singularities are also not physical objects. A physical object would have dynamical properties. If black hole singularities were to have dynamical properties, then the no-hair theorems would limit them to mass, charge, and spin. But these are not properties of the singularity but of some large region of spacetime as measured by a distant observer. The distant observer can't even say whether the black-hole singularity already exists "now."

I feel pretty secure in these conclusions, but do the conclusions about the dynamical properties of black hole singularities extend as well to non-black hole singularities? Does the big bang singularity have dynamical properties? Would a timelike or naked singularity? A conical singularity?

MTW has a nice discussion at p. 457 that explains why, for example, we can't define the total electric charge of a closed universe -- which we might have imagined we could do because the amount of matter in such a universe is finite. Does this extend to a statement that we can never define the mass, charge, or spin of any big bang singularity?

There's a famous (mis)quote from John Earman to the effect that if we had a timelike singularity, anything at all could come out of it, including green slime or my lost socks. Does this extend to a statement that we have no way of characterizing anything about such a singularity? Here we have a failure of global hyperbolicity, which is sort of a breakdown of the entire enterprise of physics. In the absence of global hyperbolicity, it's hard to see how we can define any sane properties for anything, except perhaps in some local region of spacetime that is at a safe distant from the misbehaving regions.

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# Do non-black hole singularities have observable properties?

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