Group of close orbiting neutron stars and event horizon

[Moonbread]

The average denisty of a black hole scribed by the event horizion drops with its total mass(what could happen as its desity approaches zero?) . Ive seen people express blackhole density in earth ATM with the largest hole discovered so far was described at about 22 ATM. Any way would a group of very close stable orbiting nuetron stars in some roseta form an event horizon? If not then a shit ton more mass can occupy a given volume of space then even a sigularity can cram, right?

[granthutchison]

Trouble is, if they're in a stable orbit, they've got to be farther apart than the size of the black hole that would be created from their combined masses - so the density of any such stable system is less than the critical black hole "density" mentioned in your question. And if you move them close enough together to reach the critical "density" for a black hole to form from their combined masses, an event horizon will appear around them, but there will no longer be any stable orbits for them to follow - all free-falling trajectories inside the event horizon hit the black hole's singularity in a finite time measured along that trajectory.

(Though in general relativity "stable orbit" is a relative thing anyway, because such close associations of neutron stars are measurably losing energy by gravitational radiation, so they eventually spiral into each other.)

Grant