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My understanding is that there are credible theories out there in which the formation of a singularity in a black hole also represents the beginning of a new universe via a big bang. We can't see the new universe because we can't see anything from within a black hole. Further, the apparent size of the black hole to us does not have to equal the size of the new universe from the perspective of someone inside that universe. My question is, is mass+energy conserved? That is, is the total amount of material within the new universe limited to how much stuff has fallen into the black hole, or how much stuff has reached the singularity? If so then it would seem these black hole universes are only a tiny fraction the size of our own universe.

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    $\begingroup$ This is really, really, really, speculative. $\endgroup$ – HDE 226868 Jun 1 '15 at 20:09
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is mass+energy conserved?

Yes. Even in general relativity energy and momentum are conserved, although it is a bit more complicated than in Newtonian Mechanics.

is the total amount of material within the new universe limited to how much stuff has fallen into the black hole, or how much stuff has reached the singularity?

No. Well, sort of. The physicist who's work you linked in your question addressed this in a follow-up paper. His original work (about which your article was based on) is: Cosmology with torsion: An alternative to cosmic inflation. A follow-up discussing the mass of the new universe is: On the mass of the Universe born in a black hole. In this paper he claims if our entire universe were inside a black hole, the black hole would only have to be 1,000 solar masses.

Believe it or not, this doesn't violate conservation of energy. In fact, he explicitly uses conservation of energy in his calculations. The resolution of this paradox is that there is A LOT of energy in the gravitational field of a black hole.

In this model, the singularity inside the black hole never forms. An event horizon forms as the matter collapses, as you would expect, but inside the horizon space-time "bounces" before it has a chance to make a singularity. As the matter falls inwards its energy increases; it accelerates and increases its kinetic energy due to the immense gravitational field. When it reaches the stationary "universe" inside this kinetic energy is translated into rest-mass energy: and if the matter was accelerating for long enough the increase in energy can be enormous. This gives the "universe" inside potentially a lot more mass than the stuff that fell in. This process is described in the paper as the creation of particle-antiparticle pairs by the gravitational field, which amounts to the same effect. Either way, you take energy from the gravitational field and turn it into the energy (mass) of particles inside the horizon. Someone sitting outside the black hole doesn't notice this, because they can only measure the total energy and that remains constant.

If so then it would seem these black hole universes are only a tiny fraction the size of our own universe.

Not quite. Inside the event horizon the crazy warping of space-time can make the inner "universe" quite large. Like the TARDIS, something much bigger on the inside :)

I am obliged to say that all of this work is very theoretical, his conclusions rest upon some assumptions that we have no evidence to support, but its a neat idea!

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Under the assumption that there is some sort of "Big Bang" scenario, then we are assuming an expanding universe. General relativity does not require the conservation of mass-energy on a universal scale in a changing spacetime (arguably, GR doesn't even have a concept of energy on a universal scale), so there is no a priori reason why this black-hole-universe cannot be comparable to our own (in whatever senses we pick).

A simple way to see why energy conservation must be violated, even in a vaccuum, is to first observe that the vacuum energy density is fixed. So if spacetime is expanding (or contracting), then we are changing the total volume without changing this vacuum energy density. Keeping the density the same but increasing the volume means more total energy; decreasing the volume with the same density means less total energy.

We can also easily observe this violation. You may be familiar with the concept of redshift: light coming to you from a source that is moving away from you (or emitted from a gravitating source) is shifted towards the red side of the spectrum. This stretches out the wavelength, so the light has less energy. The energy doesn't go anywhere, it's just gone.${}^*$

We might also note that, with Noether's theorem in hand, we know that time translation invariance implies conservation of energy. But a non-static spacetime is inherently not time translation invariant, so conservation of energy is not required.

${}^*$ Well, some may try to regain conservation of energy by asserting that there is an energy of the gravitational field to consider. This isn't adopted by everyone, but it can be done if you're careful with your definitions. It just doesn't work as generally and easily as you might naively hope for.

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  • $\begingroup$ +1 Can you add any references that could help the OP dig deeper? $\endgroup$ – andy256 Jun 2 '15 at 0:06
  • $\begingroup$ Your footnote is incredibly important. No, conservation of energy in general relativity is not as trivial as in Newtonian mechanics, but there IS a set of conserved quantities corresponding to the energy and momenta of matter plus the gravitational field. $\endgroup$ – Geoff Ryan Jun 2 '15 at 4:06

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