# On black holes, Hawking radiation and gravitational atoms

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.

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I'm a little nonplussed with the multitude of views this question has had but next-to-no votes or comments. If you find the topic interesting, please up-vote to further the questions popularity and stimulate people answering. Otherwise, any comments of your thoughts are most welcome. Any answers to part-questions would also be much appreciated. – qftme May 6 '11 at 19:14
You've done a lot of research and you deserve an answer, however, pleading for an up-vote isn't the right way to get one. – Michael Luciuk May 6 '11 at 20:07
re: the extra-dimensionality: string theory is inconsistent in four dimensions--the extra dimensions are necessary to create a consistent theory. As for black hole evaporation,as far as I know, I don't think that anyone has solved the Hawking radiation back-reaction problem (except for one very specialized case),and I've always been confused as to where these "times of evaporation" come from, as the method Hawking used isn't really going to be accurate once the mass in Hawking radiation approaches the order of magnitude of the hole's mass (but maybe someone's solved the bakc reaction problem) – Jerry Schirmer May 6 '11 at 21:29
@qftme Your questions require time consuming answers from experts. Most of us are not working in this field though may have some framework for answering some of the questions. For example I "know" that particles are vibrations on strings ( or equivalent more complicated constructs) and the energies of these vibrations go all the way up to the masses of black holes. My knowledge is encyclopaedic so I cannot undertake an answer. You might enjoy searching motls.blogspot.com where Lubos has many expositions on strings etc. – anna v May 7 '11 at 4:27
@Michael Thanks for your comment, honestly I didn't mean it to come across that way. Actually I was concerned that some readers might feel too timid to comment for whatever reason. As a non-professional I would genuinely appreciate any and all thoughts / comments. That said, and having re-read my previous comment, I agree that it could have been better worded. As such, I apologize. @anna I agree with your comment also. Do you happen to know anything about how a micro black hole would decay, and how this might be observed? – qftme May 7 '11 at 16:27

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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Hawking radiation is regarded as true if black holes are true, and we understand event horizons, and they exist in nature. This is because, assuming all that, we already know the vacuum is full of the foaming in and out of existence of pairs that immediately annihilate each other. So it becomes a statistical fact that sometimes these pairs will manifest near an event horizon, and before they can destroy eachother one is sucked to the other side of the EH. Hence the other one becomes evaporation.

But it can't be relied on...because there could be any number of reasons why pairs to manifest that close to the EH. Hawking recently changed his mind about event horizons...he no longer believes they exist. A firewall effect prevents it from happening.

I know what you say is correct that conventional wisdom has it hawking radiation has it in for mini-black holes. But is that even true? Does the vacuum immediately at the boundary of atoms produce pairs? Should be testable whatever the answer is. Pairs don't have a lot of surface area to interact with if the blackhole is atom sized.

The truth is, black holes as we understand them may not exist. People get shirty about that because we know for a fact things that are black and super-massive exist because we've observed incontrovertible evidence.

But that's not in dispute. No one denies the black things are there. But how much is really understood. nothing at all about the innards. Theory of formation is now snookered by primordial universe observations. No one has ever simulated a graphical of a supernova even giving rise to a black thing. Their behaviour is throwing up bizarre mystery on a monthy basis. We don't understand their behaviour. We didn't predict the Jets and we don't understand now how they happen. It's easy to say it's the accretion disc but there are serious problems with that model.

So we do actually know? Basically the hard knowledge is all the theoretical work that's been done, that hasn't been confirmed or denied by observed phenomena. Not confirmed or denied. Everything that has been confirmed or denied...has been denied (requiring major rethinks and rehashes).

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