Is mass+energy conserved when a new universe forms inside a black hole?

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!