Are black holes (and the universe in general) said to exhibit Ostwald's Ripening?

Question

Ostwald's Ripening is a phenomenon where the surface area to volume ratio of droplets causes small particles to shrink until they disappear and for droplets above a certain volume to continuously grow. This is due to mechanisms of evaporation and condensation, which I don't fully understand in this specific case. My first thought upon hearing this is "this sounds like black holes".

Hawking Radiation is a mechanism through which a black hole emits matter-energy from its event horizon. The power of this radiation is related to surface area, and in a naive sense, surface area is proportional to mass. This is as opposed to a 2/3rds power in the case of an incompressible drop held together by surface tension, but it's still monotonic and increasing which is what matters for the law to apply. Thus, all black holes are radiating, but small ones are doing so at a much greater rate relative to their mass. There is also a certain cutoff beyond which the temperature of the black hole is lower than the Cosmic Microwave Background (CMB) so the radiative balance can only permit it to grow bigger.

I'm surprised to not find any real mention of Ostwald's Ripening and black holes in the same paper. Has this terminology ever been entertained by physicists? I think Ostwald's Ripening is a physical law, although I might be trying to apply it in a cross-disciplinary sense.

Perhaps it's also valid to ask if this applies for cosmology in a larger sense. If the current thinking is to accept an apparent inevitability of a big rip, would the swelling and consolidation of black holes continue indefinitely, or would a lowering of the CMB due to the universal acceleration cause all black holes to evaporate way in the future? Is this question trivial or non-trivial?

Answer 1

Ostwald ripening isn't a "law" in any usual sense of the word.

In general a colloid is in dynamic equilibrium with a finite concentration of the solute. Small particles/droplets have a higher surface energy to mass ratio simply because their surface area to volume ration is higher, so it's energetically favourable to transfer material through the solution to the larger particles. This means large particles/droplets tend to grow while the smaller ones shrink. This is the phenomenon of Ostwald ripening.

I suppose this is sort of similar to black holes. If you maintain a bath of background radiation between the temperature of small and large black holes the small ones will shrink, heating the background, and the heated background will then enlarge the big black holes. However it's not clear there is anything useful to be gained from looking at black holes in this way.