When I was in college, Gerhard ‘t Hooft (a Nobel-prize winning physicist) came to speak, and gave a lecture on black hole evolution (I think based on this paper). I didn’t have the education to really understand it, and I still don’t, but what I got out of it was

- Hawking radiation is a semiclassical approximation
- A black hole in a box should be coherent, just like Schrodinger’s Cat
- Therefore Hawking radiation is really just the stuff that went in to the black hole coming back out, after a lot of interactions

This felt right to me. Call it parsimonious: if you can explain all expected black hole behaviors within the existing laws of physics, then that’s probably the right answer. It does, however, force you to throw out the no-hair theorem, which states that black holes are a perfect billiard ball, smooth and free of history. That might be true in General Relativity, but it can’t be true in coherent quantum gravity.

One interesting side effect of this approach is that all the various conservation laws should apply: not just the classical ones like conservation of energy, momentum, and charge, but also quantum ones like color charge, weak isospin, baryon number (i.e. # of quarks), and lepton number (~# of electrons).

This is not normally a problem. We can simply demand that the Hawking radiation spit out the same proportions of stuff that went in in the first place. No Big Deal.

A few months ago, the first gravitational wave detection was announced. A billion light-years away, a 36-solar-mass black hole merged with a 29-solar-mass black hole, in a collision so dramatic that 3 solar masses of energy were radiated away as gravitational waves, leaving a 62-solar-mass black hole behind, spinning rapidly. Conservation of mass/energy, check. Conservation of angular momentum, check.

But what about baryon number? Ordinary matter falling into the black hole is almost entirely baryonic by mass, insofar as it’s mostly protons and neutrons. Five percent of the mass was lost to gravitational waves. That means the Hawking radiation would have to produce the same number of baryons, at a 5% discount on mass! If the Hawking radiation is protons and neutrons as seems natural, then this is simply impossible. The mass of a proton (or neutron) is a constant.

I can think of several ways to resolve this problem, all of which seem implausible.

The baryons could come out bound in low-mass configurations The lowest-mass configuration known is Iron-56, which has a 1% mass discount … not even close to enough. The only known way to pack more baryons into less mass is to spit out an entire gravitationally bound neutron star … which would be an awfully big piece of Hawking radiation!

We could assume that at least 5% of the mass was contributed by the kinetic energy of infalling particles. This is probably true … but it doesn’t seem like there’s any reason it *has* to be true. If we carefully fed two black holes with low-speed baryons, would they then not be able to radiate gravitational waves upon colliding? That would be extremely weird, a gross violation of general relativity.

It turns out that baryon number may not be conserved. However, most existing theories assume some similar conservation laws. Even if baryons can be converted into leptons, the finite mass of the lightest lepton (neutrinos) means that proton-fed black holes will still run into this problem if they radiate enough of their mass into gravitational waves. Sure, it’s unlikely, but it still doesn’t seem like an expected limit. Moreover, the validity of quantum coherence and general relativity shouldn’t depend on the fine details of high-energy conservation laws!

Finally, we could postulate that baryon number or other quantum numbers could be carried away *by the gravitational waves themselves*. If the wave were absorbed by another black hole, it could even transfer the quantum number into that black hole, for eventual re-emission. This is the most beautiful solution … but also the weirdest. Firstly, this is weird because all existing quantum gravity theories assume a simple massless graviton as the force carrier. How do you encode a baryon or lepton number into a graviton!? Secondly, this is weird because essentially all gravitational wave mass energy will radiate to infinity, dissipating and redshifting with expansion. Where did the baryons go? You can’t redshift the mass of a proton!

I must be misunderstanding ‘t Hooft, but I’m not sure how. (I certainly can’t decipher the paper!)

I wonder if anyone else has thought about this.