# Spaans, “On Quantum Contributions to Black Hole Growth”

This paper was posted to arxiv a couple of weeks ago: http://arxiv.org/abs/1309.1067

From the abstract:

The effects of Wheeler's quantum foam on black hole growth are explored from an astrophysical perspective. Quantum fluctuations in the form of mini (10^-5 g) black holes can couple to macroscopic black holes and allow the latter to grow exponentially in mass on a time scale of ~10^9 years. Consequently, supermassive black holes can acquire a lot of their mass through these quantum contributions over the life time of the universe.

Is this paper at all believable? The thing that immediately bothers me about it is energy conservation. He doesn't have a real theory of quantum gravity, so this is some kind of semiclassical argument based on two theories: GR and quantum mechanics. GR has conservation of (mass-)energy in an asymptotically flat spacetime. Quantum mechanics has conservation of energy. So how can he put these ingredients together to get a prediction that seems to violate conservation of energy?

He says,

These mini BHs acquire their mass from the huge Planckian vacuum energy and not the BH itself.

I don't see how this gives him a free pass on conservation of energy. The vacuum's energy should be a function of its state, and its state isn't undergoing some monotonic change over time.

• I don't know enough about the validity of the result, but vacuum energy $\propto$ volume of vacuum, and as the mass of the black hole increases, so does its radius, and thus, so does its volume, so the volume of the exterior of the black hole decreases. This is, of course, a flimsy argument, though. – Jerry Schirmer Sep 12 '13 at 3:38
• For those not familiar with the astrophysical motivation: There is indeed some tension in that we observe SMBHs in high-$z$ galaxies, where they would not have had much time to form. This is exacerbated when you consider that quasars are generally believed to have duty cycles - they are not always accreting. Of course, there are plenty of more mundane astrophysical explanations that have yet to be tested or ruled out. – user10851 Sep 12 '13 at 6:14