Black holes to the rescue

We contine with an explanation of why Stephen Hawking is famous among physicists.

Our astronomer writes:

Last week I left a terrible mess.  Stephen Hawking had proved that singularities in space-time were unavoidable, and thus that mathematical physics was in peril: one cannot tell, even in principle, what will come out of a singularity.  The assumption on which astronomy had been based since at least Ptolemy (two thousand years ago), that we can predict motions of heavenly bodies, was in doubt.

But we seem to be saved by black holes.  These are objects that reach a certain density, a sufficiently strong gravity, so that even light cannot get out.  They were hinted at in Newtonian physics, but were only fully developed with Einstein’s General Relativity, the basis of Hawking’s work to this point.  For the problem of singularities, their importance lies in their event horizons.  Nothing behind these horizons can affect what lies outside.  And all the singularities that scientists have managed to calculate lie behind an event horizon.

Are they always hidden?  That’s the “Cosmic Censorship Hypothesis,” that there are no naked singularities.  After many years, and in spite of its importance, we still don’t know if it’s true.  Hawking himself changed his mind on the matter at least once, and as yet there are no proofs (or disproofs).

But black holes have other interesting features.  For instance, if two of them meet and merge, the area of the event horizon of the result will be larger than or equal to the total of the separate ones.  That sort of one-way increase is rare in basic physics, but suggests (to a certain kind of mind) something from thermodynamics.  In a closed system, entropy always increases.  Do black holes have entropy?  That would be almost as disruptive as a naked singularity, because nothing comes out of a classic black hole: it must have a temperature of absolute zero.  Zero temperature and some entropy is a combination that, to say the least, is hard to work with.

Enter quantum field theory.  According to this (phenomenally successful) way of calculating things, particles can pop out of nowhere in matter-antimatter pairs, exist for a (very short) time, and disappear by annihilating each other.  There are subtle effects of these “virtual particles,” but mostly one ignores them.  However, if a virtual pair pops into existence near a black hole, one of them may fall in.  If the other does not, it’s left without something to annihilate with.  It can escape.  In effect, the black hole is a source of matter/energy.  This is Hawking radiation.  It’s far too weak for us to detect for any black hole we know of or suspect, though people do calculations about possibilities in the very early universe.  But it makes the field of black hole thermodynamics consistent, fitting in with the rest of physics.

Now, Stephen Hawking did not prove all the singularity theorems himself, nor did he produce black hole thermodynamics single-handed.  I don’t want to give the impression that he was a lone genius.  But I remain astounded at someone who had such a grasp of General Relativity, Quantum Field Theory, thermodynamics and mathematics–subjects taught separately in grad school–that he could put them all together.  That, it seems to me, is the basis of his fame.