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I am not talking about event horizons. I am talking about the actual remnant of stellar collapse.

Is it just a point, hence the problem with the singularity? Or does it have a finite volume that we can infer from observable quantities?

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Nobody knows for sure. If you take a look at the mathspages Formation and Growth of Black Holes you can read about two different interpretations of general relativity:

"Historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originially conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock asymptotically approaches 'full stop'...."

If you think one interpretation is correct, you will say black holes consist of a point singularity. If you think the other is correct, you will say the black hole consists of some non-zero volume of matter/energy. For myself, I side with the latter because the alternative means going to future infinity and back and being in two places at once as per the elephant and the event horizon.

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  • $\begingroup$ NB: using > Historically... (i.e., greater-than symbol & a space before words) will give you a block quote of the passage, rather than using italics & quotes. $\endgroup$ – Kyle Kanos Jul 24 '15 at 13:16
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    $\begingroup$ John do you know anything about Kevin Brown, aside from that he's evidently a prolific writer? $\endgroup$ – Selene Routley Jul 24 '15 at 13:44
  • $\begingroup$ Rod: I know he values his privacy! @Kyle Kanos: yes I know. I tend to use that when I'm quoting the OP. I often do. Maybe I'll use it for quotes like the one above. $\endgroup$ – John Duffield Jul 24 '15 at 17:49
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Although General Relativity is used to calculate effects of strong gravity fields, and has passed all tests we can do so far, we don't know about black holes as GR cannot deal with quantum level events, which a black hole may turn out to be. We have lots of theories based on GR: (wormholes, other dimensions in this universe, other universes, etc...) but no experimental evidence to date.

So the spatial extent of black holes, if they have any, is still a mystery to us.

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