Over the past hour or so I've been following one of my standard physics-based, wanders-through-the-internet. Specifically, I began by reviewing some details of dark energy theory but soon found myself pondering a totally unassociated topic..
One of today's tweets by #arxivblog concerns a speculative (IMO) paper about the possibility that "Mini Black Holes Could Form Gravitational Atoms". I read the article on it (here) and a few of the comments and soon became perplexed by how it contradicted something I already knew. Namely, small black holes don't last very long so how-on-earth (or in space) could one "of about 10 to 1000 tonnes" exist long enough to capture a passing particle into a quasi-stable orbit? (I was recalling something I'd read about possible micro black holes, being produced at the LHC, and subsequently dissapearing in a tiny fraction of a second, due to Hawking radiation.)
~ My first question is therefore do these micro black holes decay in a particle-like fashion or does Hawking radiation theory have significant consequences on the possible decay channels?
A little more digging and I soon found that the lifetime of a black hole is $ t_{l}=M^{3}/3K $
Where $ K=h .c^{4}/30720.\pi^{2}.G^{2}=3.98\times10^{15} kg^{3}/s^{-1} $
Giving, for a mini black hole of mass, $M=100\times10^{3}kg$, $ t_{l}=0.084s $
Which, I'm sure you'll agree, is clearly too short to allow anything that could meaningfully be described as a gravitational atom. (Incidentally, my calculation for the lifetime of an LHC black hole gave something of order $10^{-94}s$!!)
Just then, the resolution to this apparent contradiction dawned on me - the above formula is derived from the radiated energy given off by a black hole via Hawking Radiation. Conversely, the paper in question is written from an initial, unstated, assumption that Hawking Radiation does not exist.
~ This led me wonder, to what extent is Hawking radiation accepted amongst professional theorists? (I'm aware that it has not yet been directly prooven, so consideration of the implications of it's non-existence must surely be worthwhile, and interesting, IMO.) I realise this question is somewhat vague but I am hoping for some elucidation on how firm-a-foundation Hawking first derived this phenomena and, given it is based on QFT bolted-onto a curved spacetime, has modern developments (in for example, String theory) corroborated the possibility of energy loss over the event horizon in this way?
~ A quick glance at the wiki article on primordial black holes (here) informed me that the Fermi Gamma-ray Space Telescope (GLAST experiment), launched in 2008, is hoping to find evidence of primordial black holes:
"If they observe specific small interference patterns within gamma-ray bursts (GRB), it could be the first indirect evidence for primordial black holes and string theory."
The reference to string theory appears only to concern the longer predictions of the primordial back hole's lifetimes; based on the extra, 'rolled-up' spatial dimensions posited by some/all(?) string theories (AFAIK due to gravity being able to propagate in these extra-dimensions).
~ Finally, therefore, if GLAST does/has find/found certain characterists in GRB data, how strongly does it (will it) rate as evidence for or against: the existence of primordial black holes, the existence of Hawking radiation and indirectly as evidence for String theory? I have had a look at papers relating to recent GRB data from the LAT experiment (here for eg) but, as a non-specialist, it is very unclear to me whether the data has any implications to the questions posed above.
Answer
Hawking radiation is a very robust prediction. It comes simply from applying quantum field theory in the curved space-time near the event horizon. It's also part of the synthesis called "black hole thermodynamics", for which string theory provides an explanation in terms of the statistical mechanics of microstates. In the S-matrix of quantum gravity, if black holes didn't evaporate, they'd show up as asymptotic states, but they don't. (There are eternal black holes in anti de Sitter space, but they still evaporate, they just don't get to evaporate completely; the particles produced by the evaporation can't escape to infinity because of the peculiarities of AdS geometry, and fall in again.)
So denying the existence of Hawking radiation would screw up many other things. You could say that Hawking radiation is real but that it falls back in, like in AdS space, but there's no reason for it to do so. The paper featured at arxivblog is a "what if" paper which ignores all these problems and proceeds to calculate some of the consequences. You could compare it to an engineering study of one of M.C. Escher's impossible structures: if you ignore the contradictions in its design, maybe you can calculate some of its properties, but it only has recreational value to do so. We don't quite know that a nonevaporating quantum black hole is logically impossible, in the way that we know the impossible staircase is impossible, but in the future a genuine proof may be available.
But empirical confirmation of black hole evaporation is rather unlikely. If we could produce mini black holes in colliders, then we'd see it, but those models aren't especially favored; they are a "what if" of a different sort, one in which there is at least a consistent fundamental picture behind the hypothesis (particular braneworld models), but it's just one of many possibilities about what happens at the next frontier of physics and those models are not significantly favored. (These models are also the ones which predict a detectable signature in GRB data.) If we could send a probe to the edge of an astrophysical black hole, maybe the radiation could be detected, but that is a job for interstellar civilizations, if they exist.
Maybe you could find indirect evidence for Hawking evaporation of primordial black holes in the cosmic microwave background. But I don't know how likely that is - again, it would be highly model-dependent.
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