My own summary of Stephen's main scientific contributions:
1) Penrose-Hawking singularity theorems, 2) Black hole thermodynamics (Hawking and Bekenstein) 3) Wave function of the universe (Hawking and Hartle)
1) Penrose-Hawking singularity theorems, 2) Black hole thermodynamics (Hawking and Bekenstein) 3) Wave function of the universe (Hawking and Hartle)
1) Roger Penrose showed that Einstein's GR ensured that there would be singularities (regions of infinite density) once certain conditions were met - black holes really form. Stephen showed this was also true of the Big Bang, there was no way of avoiding an initial singularity
(That applies, of course, in "classical" GR. In quantum gravity - the theory we still don't have - we expect to avoid actual infinities, and replace them with weird Planck quantum foam thingies. I think.)
By the way, the singularity theorem work was Stephen's PhD thesis.
2) Hawking showed that quantum effects mean that black holes are not perfectly black - they glow ever so slightly with escaping particles. They have a temperature - and they have entropy.
This 'Hawking radiation' is tiny tiny - completely dwarfed by incoming material in typical real astrophysical contexts. It would take 10 to the power 60 years for a solar mass black hole to completely evaporate due to Hawking radiation.
That's 100000000000000000000000000000000000000000000000000 times older than the age of the universe so far. Isn't being a theorist fun?
In principle you could make a small black hole - say, with the mass of a mountain - and for it, Hawking radiation would be very important (think very, very, very large explosion and gamma ray burst).
But even if we never see HR, it is important in principle because it stops black holes breaking the Second Law of Thermodynamics, one of physics' core principles. And even better, it hints at a deep deep connection between thermodynamics and gravity, previously unsuspected
That connection underlies a lot of the recent work on quantum gravity and holographic principles and so on (none of which I understand) and I think it's the ticking time bomb in Stephen's legacy which a future generation of theorists will see go off...
3) When I was a student at Cambridge, Stephen was working on applying old style (Feynman) path integral quantum mechanics to the universe as a whole. I love this approach, but I confess it is super not clear that it can actually describe the universe we happen to live in
The idea here is that in quantum, we write down a 'wave function' for a system - say, an atom - that tells us the probability that the atom will go a particular way and do a particular thing. We then use this function...
.. to average over all the possible ways of getting from A to B, weighted by how difficult they are, and get the probability that the atom will actually go from A to B.
Instead of looking at how an atom might travel in space, Stephen used the same approach to look at how our universe might "travel" in the space of all possible universes
He would then calculate the quantum probability that our universe would evolve from universe A to universe B.
Unfortunately his method only worked well if you multiply the time axis by the square root of -1 - Stephen's "imaginary time" and some worry that when you transform back at the end, it might not be valid. Worse,....
... in order to find a problem he could solve with these equations, he had to adopt the so-called "no boundary" condition which ends up, as I understand it, requiring a closed (recollapsing) universe - still an observational possibility in 1983 but now definitely ruled out
There were other approaches to quantum gravity being worked on at the same time - loop quantum gravity, Regge calculus approaches, buzzword buzzword. I didn't understand them at the time and certainly don't now. Penrose at Oxford, Chris Isham at Imperial, Witten etc ...
... so the popular idea that Hawking stood (at least in reputaton) head and shoulders above the rest of the community isn't really true. Primus inter pares, perhaps. But he attacked the big, deep questions and his contributions changed the field.
So that's my attempt at saying what Stephen did. I look forward to corrections or alternate views from others in the field. Really, I mean it - give me your take!
