Relation between quantum fluctuations and vacuum energy?

[vanhees71]

Yeah, real big, because otherwise we have no chance to detect Hawking radiation. However, if we come too close (which I guess we should to detect the radiation), maybe we have no time to write the paper publishing the discovery ;-)). Anyway, I guess Hawking radiation is a safe place to make theoretical predictions, because it's very unlikely to be disproven empirically ;-).

 

[George Jones]

Yeah, real big, because otherwise we have no chance to detect Hawking radiation

But the Hawking temperature of a black hole is inversely proportion to mass, and power radiated goes as T^4. The temperature of a solar mass black hole is far, far lower than the 2.7 K CMB temperature, so something much, much less massive is needed in order to be detectable.

 

[A. Neumaier]

But the Hawking temperature of a black hole is inversely proportion to mass, and power radiated goes as T^4. The temperature of a solar mass black hole is far, far lower than the 2.7 K CMB temperature, so something much, much less massive is needed in order to be detectable.

Far away from a black hole of typical astrophysical size, Hawking radiation is indeed completely swamped by the microwave background radiation, while small black holes that have a higher Hawking temperature are not radiating enough to be detectable from far away. Since the intensity of Hawking radiation decays with distance like $r^{-2}$ it is not detectable unless one is reasonably close to the black hole and a lot of radiation is produced, which in turn requires a high gravitational field and hence a big black hole.

But one can study in the lab Hawking radiation in so-called analogue black holes, optical analogues where nonlinear optics simulates a quantum metric; see Hawking radiation from ultrashort laser pulse filaments:

the same physics that underlie black hole evaporation in the form of Hawking radiation may be found and studied in other, more accessible systems. Our measurements highlight spontaneous emission of Hawking radiation from an analogue event horizon generated by an “evaporating” refractive index perturbation and suggest a path towards the experimental study of phenomena traditionally relegated to the areas of quantum gravity and astrophysics.

There are also acoustical analogue black holes; see, e.g., http://arxiv.org/abs/1410.0238.

 

[vanhees71]

Well that are analogues but not the true thing. In this sense you could say that we have discovered all kinds of "exotic" particles like anyons, magnetic monopoles, Majorana and Weyl fermions,... However all these are, of course, no elementary particles but quasiparticles in condensed matter physics :-).

 

[Demystifier]

We can be lucky, it would require a very big black hole close to us...

Well, Hawking radiation is much easier to detect for a small black hole.

EDIT: Now I have seen that George Jones already said that.

 

[A. Neumaier]

Well, Hawking radiation is much easier to detect for a small black hole.

But only when you are very close by. And we don't have experimental evidence of small black holes close to us.