Before I go do a week of numerical simulations...
In our 3+1D spacetime, gravitationally-bound systems of large numbers of particles, like stars in globular clusters, can be stable for long periods, but are ultimately subject to gravothermal core collapse.
Assuming stars are collisionless, are things qualitatively similar in other dimensionalities?
There's no escape velocity in 2+1D, so stars can't "boil off" entirely, but gravitational systems still have negative heat capacity, so it seems like it should be possible to end up with a dense core and diffuse halo of lower-mass stars anyway. But since it's harder for an "ejected" star to avoid falling back into the core region with the reduced degrees of freedom, I could see it taking longer for the catastrophic segregation to take place.
In 4+1D, there are no stable 2-body systems, so a cluster not immediately collapsing or exploding would depend on each star feeling not the fundamental $r^{-3}$ gravity of a point mass, but the effective higher-exponent force from being embedded in a medium of other stars (resulting in an effective spring potential if the mass distribution is uniform). Would that be enough to stabilize a cluster, or should I expect low-mass stars to immediately start boiling off until the core completely collapses?
(And if this somehow isn't something that has been investigated yet, should I do a full 4+1D simulation, or would it be suitable to just run everything in 2+1D with differing force laws?)
