My question is, when a compact star collapses to form a black hole, how does it manage to dispose of the heat necessary to make this transition? Naively, it would seem that the object can never cool itself fast enough due to increasing gravitational redshift of its thermal radiation. Each radiated photon's energy is reduced by a factor of 1/(1+z) and the apparent rate of photon emission is reduced by 1/(1+z), so the total energy flux out of the object is reduced by a factor of 1/(1+z)^2. Furthermore, the solid angle through which each surface element's radiation can escape to space decreases with redshift, as more and more emitted light is bent back inward toward the object. If I'm figuring right, that solid angle is reduced by a factor of 1/(1+z)^2 in the limit of high z. That makes a total factor of 1/(1+z)^4 reducing the radiative energy flux out of the object. Once z is high enough that energy flux out of the object is equal to incident energy flux from distant stars and the cosmic background, it would seem that the object cannot cool itself any more. Unless there is an endothermic reaction of some sort taking place, I don't see how the star could contract further without expelling heat into space, so it would seem that the collapse cannot proceed beyond this point. Thus z remains finite and an event horizon never forms. Having read some of Abhas Mitra's papers and critiques of them, the consensus appears to be that black hole formation is NOT forbidden by thermodynamics, so what is wrong with the above argument?