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What is the theoretical limit to density? At what point could space no longer contain any more mass?

  • at absolute zero
  • assuming you could pack matter (hydrogen, a heavier atom, or a combination) so that no voids remain (like fitting golf balls, jelly beans, sand, and water into a container)
  • contained so it doesn't blow apart
  • isolated so it doesn't form a black hole that swallows our universe.

I did not think "Is there an upper theoretical density limit?" had the right flavor to it, and "A Universal Upper Limit on Mass Within a Radius $R$?" is too deep for me.

KA_
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    So you want a very high density, without a black hole? Does that, I ask rather than state, not leave you with neutron star levels of density? –  Sep 29 '17 at 15:32
  • The maximum mass in a given volume is given by the Schwarzschild radius of a black hole of that mass. Below that mass you won't have a black hole, above it, you will. – A. C. A. C. Sep 29 '17 at 16:21

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As far as I know, neutron stars meet your definition of "packing matter as tightly as possible", with a density around $10^{17} \rm{kg/m^3}$

Floris
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  • Would that increase if it were cooled to 0K? – KA_ Oct 02 '17 at 15:00
  • @KA_ I honestly have no idea what "temperature" would mean for a neutron star. But I suppose that if there is excess internal energy, it might affect the density. But this is not my area of expertise. According to this the emission of neutrinos does cool the neutron star. – Floris Oct 02 '17 at 16:01
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    Well, with a little napkin math, I came up with $(1/r)^3m = 1.8610^{17} kg/m^3$ using a neutron's radius and mass. – KA_ Oct 03 '17 at 13:01
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I also thought about that already. What I figured out is that firstly, in General Relativity, there is no such thing as a density where a black hole is created; it just depends on how much mass you have in what radius (you could e.g. create a black hole the density of air, as long as the volume is big enough), so that is no limitation (it would be in the second question you mentioned). Absolute zero isn't a problem either. The Pauli exclusion principle may cause problems, so it would be wise to use bosons (photons, Higgs particles,...). Furthermore, the amount of energy you will need to contain it all may pose problems. I would say that there are no limitations in principle, but I really am not sure.

Markus Zetto
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  • I meant this as a hypothetical scenario, so assume you have the energy to power this hypothetical containment system. The black hole remark was meant to be somewhat humorous. – KA_ Sep 29 '17 at 15:42