Interesting calculation. What's the situation with small black holes? I understand that the really tiny ones evaporate pretty quickly due to Hawking radiation, but what about a Moon mass black hole? ---- Also, can a black hole ever rotate so fast as to break apart? I.e., you have a really fast rotating black hole that gets additional mass & angular momentum added until it breaks apart into 2 black holes revolving about one another. There's also a movie on the internet somewhere that shows 2 black holes revolve around one another that eventually merge, because _graviational waves_ can carry off some of the angular momentum. At 12:27 PM 12/23/2012, Warren Smith wrote:

In various sci-fi stories, the wonderful substance "neutronium" plays a role. This is the superdense stuff neutron stars are made out of, except some amazing advanced aliens find a way to make or get hold of chunks of it.

For example in one fine Larry Niven story, there is a chunk of it about the mass of Earth's moon orbiting some planet, and foolish trinocs try to get it due to wrongly thinking it is a valuable slaver stasis box, thereby meeting their doom from its immense surface gravity.

So, let's think a bit about the actual properties of neutronium. Do they live up to the hopes of sci-fi writers?

They are correct it is very dense. The estimated density of the nuclei of atoms averages about dens=4*10^17 kg/m^3, which is 4*10^14 times denser than water. Thus the mass of the Moon would fit in a sphere of radius 35 meters, which I thunk is rather larger than Niven had in mind.

The problem is, neutrons are unstable. Neutron has a mean life of 15 minutes for decay into proton+electron+antineutrino+energy. The energy release for decay of a free neutron is 782 KeV (which is about 1/1201 fraction of its rest-mass energy) but for neutrons in different atomic nuclei it can differ, sometimes being as large as 1.5MeV (?).

Anyhow, for a ball of neutronium of radius=r and mass=M, we expect it should be unstable to neutron decay if the gravitational escape energy for a neutron-mass is less than 782 KeV. That is, Mcrit = dens * rcrit^3 * (4*Pi/3) and mneutron * G * Mcrit / rcrit = (782 KeV)*c^2 = 1.25290199 × 10^(-13) joules Solving, I find Mcrit = 9.2 * 10^27 kg = about 4.8 jupiter masses rcrit = 818 meter

conclusion: A chunk of neutronium smaller than about 5 jupiter masses or which fits in a ball of radius<=818 meters cannot exist; if you had one, it would explode.

Actually, even larger balls should also be unstable since we do not need the decay products to escape all the way to infinity -- our argument really only provides very weak lower bounds on Mcrit and rcrit.