Erik said: > Yeah, yeah, my mistake! Actually, I haven't done the math for a while, > but doesn't it depend on the density of the objects as well as the > total mass? If the objects aren't dense enough to begin with, isn't a > singularity impossible?
If the density is high enough that an object is within its own Scwarzschild radius then it will necessarily collapse to form a singularity. Things are more interesting if you keep adding more mass to a larger body. The gravitation will compress the centre more and more, and eventually the centre will be compressed so much that it will be within its Schwarschild radius and so will form a black hole. Calculations are a little tricky because you need to take into account thermal pressure, radiation pressure and electron and nucleon degeneracy pressures as well as radiation transport out of the body (which is, if I recall correctly, the limiting factor in the formation of stars from gas clouds). Rich GCU I Knew All This Properly A Long Time Ago
