Buzz Bloom said:
I am wondering about the division of opinions on this topic. Can you make a rough estimate of the fraction of physicists who have each of one of three logically possible opinions?
1. Hawking radiation is definitely more likely than not to be a real possible phenomenon.
2. Hawking radiation is definitely more likely than not to not be a real possible phenomenon.
3. It is more-or-less equally likely that Hawking radiation is or is not a real possible phenomenon.
I have no data about the opinions, but it looks like a majority has never heard about the trans-Planckian problem of the derivation at all and so they think Hawking's derivation is fine, thus, Hawking radiation is a certain prediction of semiclassical gravity.
There have been many attempts to find variants of the proof which do not rely on trans-Planckian assumptions. They all failed, and it is quite easy to identify the weak points. One has to know that stable stars don't radiate Hawking radiation - you obtain it only if there is a change of the gravitational field which also leads to a change of the vacuum state. Without change of the vacuum state no radiation. Then, it is sufficient to recognize that one can modify GR in the trans-Planckian domain in such a way that the collapse stops. All you need is a force against the collapse which becomes greater if time dilation (in preferred Schwarzschild-like coordinates - a modified GR can have them) becomes astronomical so that ##10^{-100}## Planck time on the surface means more than ##10^{100}## times the age of the universe for the far away observer. If in that modification the collapse stops, there will be no Hawking radiation (except during collapse time). See arxiv:0906.1768 for how fast it stops (almost immediately).
Nonetheless, who cares, once there are many many different "proofs"?
The most impressive arguments for those who are at least aware of the trans-Planckian problem are analogies. Surprisingly many accept the analogy with Unruh radiation: Acceleration leads to some similar radiation effect. Surprisingly, because it can be easily shown to be false: Stable stars don't Hawking-radiate despite the fact that they give some acceleration.
The other analogy argument which has been quite powerful (in its sociological influence, not in its argumentative strength) are "dumb holes" in condensed matter theory. The point is that they seem to circumvent the trans-Planckian problem because they have an explicit cutoff - atomic distances. Nonetheless one can show some Hawking-like radiation. What if we confront this analogy (as suggested above) with some stable configuration? We will see that all the examples of "dumb holes" have nontrivial flows, thus, even if as flows they are stable, on the atomic level they are not stable - the atoms move.
To summarize, I would not suggest to care about majority positions in physics, simply because the majority does not take care about the details. This holds in physics as well as in politics - following the majority may be a reasonable political decision if one wants to optimize the own interest, but it is not a good idea if one wants to find out the truth.