If a white dwarf compresses to the limit of electron degeneracy, and a neutron star compresses to the limit of neutron degeneracy, what does a black hole compress to the limit of?
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8$\begingroup$ We don't know... $\endgroup$– MithoronCommented Jul 18, 2019 at 20:33
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4$\begingroup$ Neither of the above statements is really true. Degeneracy is a continuous parameter and does not have a "limit" except at infinite density. The reasons that white dwarfs and neutron stars do not exist towards infinite density is not because of some limit on the degeneracy is reached, but for other physical reasons - neutronisation in one case and GR in the other. $\endgroup$– ProfRobCommented Jul 18, 2019 at 23:08
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2$\begingroup$ This answer may help you: physics.stackexchange.com/a/141876/232868 $\endgroup$– SurpriseDogCommented Jul 19, 2019 at 16:12
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2 Answers
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In classical General Relativity, there is no limit to the compression in a black hole, hence you get a singularity. However, many astrophysicists feel that's unphysical, and that a theory which unites General Relativity and Quantum Mechanics will impose some kind of limit, perhaps something connected with the quantization of spacetime itself.
We don't have a working theory of quantum gravity, so at this stage we don't exactly know what happens in the core of a black hole. OTOH, we're fairly confident that the core has to be very small, since quantum gravity effects probably don't kick in until a scale much smaller than the size of an atom, and probably smaller than a proton, somewhere around the scale of the Planck length.
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As far as current physics knows, nothing. This is the reason why it is commonly thought that a singularity exists in the middle of a black hole.
However, singularities are also thought to be non-physical, so there is most likely something else inside a black hole — we just don’t have the science to describe it just yet.
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3$\begingroup$ It's not really "commonly thought" that there's a singularity in the middle of the black hole (except in sci-fi, though that also gives you things like the event horizon being a physical barrier you can shoot your way through, so...). It's just the most straighforward result you get from applying general relativity to the problem, and assuming there's nothing beyond neutron degenerancy pressure to prevent further collapse. Not to mention the assumption that the matter actually had time to reach the "singularity". AFAICT, to a physicist, singularity is not a thing that exists - it's a mistake $\endgroup$– LuaanCommented Jul 19, 2019 at 8:04
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$\begingroup$ Exactly, I agree 100%, my wording is inaccurate as this was the exact meaning I wanted to convey $\endgroup$– tuomasCommented Jul 19, 2019 at 8:07
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$\begingroup$ @Luaan Isn't "nothing beyond Neutron degeneracy pressure" a bit misleading? My understanding is, that according to plain GR, the singularity is in the future of anything inside the event horizon, and no force (measurable in Newtons, like exerted by the degeneracy pressure) can prevent that. AIUI, this is why having new strange forms of dense matter is basically irrelevant inside a black hole in the GR, the space-time doesn't care. $\endgroup$– hydeCommented Jul 20, 2019 at 21:20
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$\begingroup$ @hyde No, there's no magic involved - the spacetime within a black hole is exactly the same as outside of the black hole (as far as plain GR is concerned). The only thing that might be different is the part we now mark as a "singularity". There's certainly nothing special happening as you cross the event horizon. Of course, you still can't go back "outside", but that's mainly because there's no path leading outside. Mind, there is truth to saying "the singularity is in the future of anything inside the event horizon"; but that's analogous to us moving through time - as is leaving the hole. $\endgroup$– LuaanCommented Jul 21, 2019 at 13:56
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$\begingroup$ @hyde It would definitely make a great question in its own right, though :) $\endgroup$– LuaanCommented Jul 21, 2019 at 13:57