Is there any evidence that matter and antimatter continuously appear and disappear on the edge of a black hole? I heard Stephen Hawking got a Nobel prize for this, someone said there was no evidence for it which I find quite strange since he got an award for it.
 A: Direct experimental evidence of Hawking radiation is going to be exceedingly difficult to obtain. The radiation from stellar mass black holes is so small as to be undetectable, and we haven't (yet) worked out how to small black holes in the lab. At the moment there is no direct experimental evidence, and we have to accept we may not see any in our lifetimes.
However we can examine systems that are described by similar mathematics to see if they show analogous effects. A few years ago a team did an experiment of this type, and they claim to have seen the equivalent of Hawking radiation. There have also been experiments looking at acoustic analogues of black holes, though I don't think they have yet seen the analogue of Hawking radiation. These experiments don't prove a black hole radiates, but they show that the type of mathematics used to predict Hawking radiation from black holes does work when applied to other systems.
A: According to the Hawking radiation Wikipedia article, there was one experiment in 2010 which the experimenters claimed showed evidence of Hawking radiation, but that claim is in doubt, and there hasn't been any other experimental evidence of Hawking radiation.  Stephen Hawking has received a number of awards and honors, but the Nobel Prize is not among them.
A: There is plenty of evidence for the underlying quantum field theoretical description of the vacuum.


*

*The (complete) quark content of the nucleons has been measured, and includes both flavors not in the valence content (strange, charm (?)) and lots of anti-quarks. Everything that isn't valence content ($uud$ for a proton or $udd$ for a neutron) is called the "sea", and it comes from the same place as the pairs that Hawking is working with. The experiments I'm familiar with are NuSea and SeaQuest, but there are others.

*Pair-production (of electrons and positrons) happens all the time in high-energy photon interactions with matter (it's one of the main energy loss mechanisms) for photons with energy much higher than 1 MeV. In principle we should be able to do this in free space in the field of a very strong magnet, but I'm not aware of a actual realization of this; lots of theory papers in the google search, but no experiments. These pairs also come from the vacuum. 

*Other kinds of pair knock-on reactions. Nuclear pion production in very forward kinematics is dominated by quark pair-production and so on.
A: If we take the idea of black holes as basically ideal black body radiators seriously, the radiation that large black holes can emit can only consist of photons. Actually, all macroscopic black holes right now should be far colder than the CMB, which means that for now they are "feeding" on the CMB, rather than emitting more radiation than they receive. 
Before a black hole can emit charged particles, it has to heat up to a very high temperature. Since an electron positron pair has a threshold energy of approx. 1MeV, the corresponding temperature should be a fraction of 11.6 billion Kelvin. 
Using the black hole calculator at http://xaonon.dyndns.org/hawking/ (no guarantees that it's correct), that temperature would correspond to a black hole of 1.05e13kg mass (which is roughly equivalent to 10 cubic kilometers of water). The radius would be 1.57e-14m (approx. 18 times proton charge radius) and it would have 3MW of luminosity (surprisingly little for "my taste") and 3.15e15 years of lifetime. 
The long lifetime of such an object will certainly allow it to survive long enough since the early universe to be still around today (assuming that it would form by some mechanism). The problem is, that a 3MW radiation source in space is way too dim to be detected from even stellar distances within the galaxy. Even if we assume that such an object could radiate away all of its mass-energy in a short amount of time, it would still only produce an extremely dim flash of gammas. For comparison, the sun radiates approx. 4 million metric tons of mass-energy per second. At that rate our small black hole has "fuel" for a mere 250,000s or less than three days! 
To me it seems extremely unlikely that we could detect such an object radiating gammas in the MeV range with any likelihood, unless, of course, the universe is choke full of them. 
If the numbers are off, I would be glad to be corrected. 
