> Evaporation accelerates until the cluster basically explodes
This sounds very much like what happens at the end of a black hole's lifetime as it evaporates by Hawking radiation. Any chance that's a real connection?
No, but also maybe yes, but it's way over my pay grade as a physicist. In short, I think the fact that gravitational systems have negative specific heat capactiy is very relevant.
As gravitational systems lose energy, the "temperature" of the ensemble of particles goes up. (I.e. objects with smaller orbits have higher velocities.)
It is probably not exactly an accident that this relationship holds for blackholes as well: the hawking radiation formulas suggest a larger and larger temperature for blackholes with smaller and smaller event horizons. The hawking radiation stuff is built upon entropy / temperature relationships so I think there is actually some kind of connection there.
There might even be something baked into the energy conditions / bianchi identities of GR that is manifesting in that way, but I'm speculating.
Well yeah, probably, but sometimes very weird analogies between systems turn out to produce real physics, and it doesn't even seem impossible to me that there's something similar happening behind the event horizon of a black hole. I'm just hoping someone smarter than me has already done the math.
There is a relationship in that both the "Spongebob cluster" and a black hole has negative heat capacity. The math is already there in the virial theorem. See <https://en.wikipedia.org/wiki/Heat_capacity#Negative_heat_ca...>. Detailed treatments of the non-relativistic case you can find in an undergrad astronomy textbook; the relativsitic singleton case ehhhhh I don't think you're ready for it but Wald's General Relativity §12.5 & §§14.3-14.4 would be a good choice (and he shows you the math, which has been known for several decades), and for relativistic orbits I think you need to go beyond textbooks (although you probably could start with numerical relativity textbooks, like Baumgarte & Shapiro or Alcubierre, although I don't have either handy to double-check where they go with thermodynamics. Oh and the paper I linked in a sibling comment has a good and relevant bibliography. <https://academic.oup.com/mnras/article/516/3/3266/6668807>).
However it's best to think of "the black hole" as the entire spacetime (in Hawking's 1974 treatment and similar; or alternatively out to somewhere in the asymptotic flatness), in which there are two regions without a horizon, one to the past of the event horizon formation, and one to the future of final evaporation.
What goes into the horizon doesn't stay in, therefore what happens inside is part of the picture (and has been speculated about for fifty years! Fifty!)
Yeah technically, in the current formulation, but I think at this point the smart money is on Hawking radiation being correlated with something on the inside. For instance this is my favorite solution for the information-loss problem, that the info is carried away by hawking radiation.
As far as I am aware the virtual particles near the event horizon of black hole behave nothing like stars in a galaxy. For a start, stars much more massive (many many orders of magnitude) and aren't influenced by quantum mechanical effects in the same way as individual particles.
This sounds very much like what happens at the end of a black hole's lifetime as it evaporates by Hawking radiation. Any chance that's a real connection?