Do Black Holes become visible at relativistic speeds?

[PAllen]

Back to the original thread topic, Peter and I discussed the visibility of Hawking radiation to an observer rapidly approaching a BH. The traditional view (pre-firewall) was presented, by among others, Verlinde in papers from the 1990s. This is the view Peter mentioned: infaller's see no Hawking radiation. On reviewing my own notes on this, I see that I had not so much forgotten this view as pushed it out of mind as no longer convincing to me. The following paper, especially, led me to doubt its truth. If this and similar ones are right, then there is every expectation that approaching a BH at extremely near c will make it's Hawking radiation increasingly visible:

http://arxiv.org/abs/1101.4382

I think a key logical argument from this paper is asking about a static observer starting free fall (rather than the simplest case typically picked: free fall from infinity). Does the Hawking radiation immediately disappear? That seems implausible, and this paper derived that it is not so. So what happens over time for free fall after having been static? This paper argues that the observed Hawking radiation increases to limiting value at horizon crossing.

 

[timmdeeg]

Because the derivation of Hawking radiation as equivalent to Unruh radiation depends on the fact that, mathematically, the black hole's event horizon is equivalent (modulo some technicalities that don't affect this discussion) to a Rindler horizon for static observers--that is, observers who are accelerating outward in order to remain at a constant altitude above the horizon. But this equivalence *only* holds for those static observers--it does *not* hold for observers with other accelerations. (Which means it doesn't even hold, strictly speaking, for observers who are accelerating outward either less or more than a static observer.)

Ok, that's a very good explanation, thanks for spending your time.

 

[PeterDonis]

Does the Hawking radiation immediately disappear? That seems implausible

But the same thing happens in the case of Unruh radiation; if you shut off your rocket engine and stop accelerating, the Unruh radiation disappears immediately.

I haven't read the paper through yet, so perhaps they address this.

 

[WannabeNewton]

That seems implausible...

Why exactly is it implausible? In flat space-time it's just a result of the Bogoliubov transformation for creation/annihilation operators of e.g. a Klein-Gordon field on the Minkowski background that if you have no particles with respect to one vacuum you will in general have particles with respect to another vacuum. The act of shutting off the rockets is the same as instantaneously transforming from one vacuum to another. The difference in particle fluctuations in vacuum is after all what leads to the Planck distribution when the rockets are not off. Why would it be any different in curved space-time?

Like Peter I too have not read the paper yet so hopefully it's addressed in the paper.

 

[PAllen]

Here is a paper referencing the one I gave earlier, validating its main results with different methodology and assumptions, and extending it to the case of circular orbits, with the interesting conclusion that a detector in a circular orbit around a BH detects more Hawking radiation than the static detector at the same radial position.

http://arxiv.org/abs/1304.2858

 

[Haelfix]

To really have a concrete picture as to what happens to Alice when she falls into the black hole, we really need a fully fleshed out model of the quantum mechanics of the near horizon degrees of freedom. What modes are being excited, how fast is the thermalization and what sort of measuring device are we using (and what local operators are we measuring).

There are some papers that try to treat this very hard question (like the one that is linked), but I believe the consensus is that they are still hopelessly naive without a real model of quantum gravity.

Again, if you claim to see a calculation of a hot horizon (eg Hawking modes, Fuzzballs, bouncing stars, Firewalls etc) the trivial thought experiment is to pick a very massive black hole (so that curvature invariants along the horizon are arbitrarily tiny) and argue based on effective field theory what is known as the adiabiatic principle/no drama hypothesis, which seems to suggest (naively) that a local observer should see departures of the equivalence principle at most up to statements that include functions of these curvature invariants, together with suppression factors that contain powers of the Planck Mass.

It is very hard to save locality and the classical theory of GR in those circumstances (eg we are talking about arbitrarily large modifications of GR at arbitrarily long distances) and although it is not unheard of for effective field theory reasoning to fail, the magnitude of the failure here would be quite unheard off.

 

[PAllen]

Perhaps they are naive, but so is the confident claim that someone accelerating toward a BH (or even free falling) detects no Hawking radiation.

 

[Haelfix]

Don't get me wrong, I am making no claims here. I have no idea what the correct statement is. It does however seem like no matter what physics we choose, that we are forced to give up something cherished, which is why there has been so much work on this subject in the past several years.

I actually believe that the hot horizon camp seem to have the strongest overall intellectual case as it currently stands, even though I suspect that one day it will go away somehow.

 

[PAllen]

I don't really see the papers I linked as being in the 'firewall camp', or proposing a hot horizon (more like a warm horizon for most in fallers, with a limiting special infaller that sees no Hawking radiation). They analyze within the semi-classical framework in which Hawking radiation is traditionally derived. Whether they correspond to what would be observed in our universe (or what would be predicted by a complete theory of quantum gravity) is obviously not known.

In any case, if these papers are taken as true, then my post #8 remains an accurate summary. Rapidly approaching a BH formed from collapse would increase its visibility due both to a classical effect (blue shift of leaking, nearly trapped, light) and a quantum effect (blue shift of Hawking radiation).

[edit: A further observation is that the papers I referenced are not really discussing anything about distinguishability of the horizon - thus Haelfix general argument does not apply. They discuss phenomena visible at a distance from the BH and the limiting behavior (temperature) on approach to the horizon. For example, observation of Hawking radiation in circular orbits of a BH is certainly not a horizon phenomenon (though, of course, the origin of Hawking radiation is related to the existence of a horizon.]

 

[tionis]

In any case, if these papers are taken as true, then my post #8 remains an accurate summary. Rapidly approaching a BH formed from collapse would increase its visibility due both to a classical effect (blue shift of leaking, nearly trapped, light) and a quantum effect (blue shift of Hawking radiation).

True. I was curious about this and someone in academia was kind enough to workout some of the details:

According to the standard picture of black hole thermodynamics, a black hole has a temperature (due to Hawking radiation). When one travels towards a black hole with a speed very close to speed of light, one is traveling with a very large "Lorentz factor" (e.g. 0.999994 c corresponds to Lorentz factor 300; and c corresponds to Lorentz factor infinity). All the light seen by you would be boosted by a factor of order the Lorentz factor. So is the black hole temperature. For a stellar-size black hole, the temperature is extremely low, say 10^{-8} kelvin. Suppose there are no stars, CMB and other luminous objects, yes, when you travel very close to speed of light, say, your Lorentz factor is 5x10^11, then the black hole temperature can be 5000 K -- this is essentially a star. Then you can "see" the black hole. Notice that the required speed is really close to c: 0.9999999999999999999999992 c!

^^That's hot!

 

[Haelfix]

[edit: A further observation is that the papers I referenced are not really discussing anything about distinguishability of the horizon - thus Haelfix general argument does not apply. They discuss phenomena visible at a distance from the BH and the limiting behavior (temperature) on approach to the horizon. For example, observation of Hawking radiation in circular orbits of a BH is certainly not a horizon phenomenon (though, of course, the origin of Hawking radiation is related to the existence of a horizon.]

I finally had a chance to read 1101.4382, and you are correct. The paper is really dealing with a semi realistic collapsing geometry, rather than the case of an eternal Schwarzschild black hole (so Hawking radiation switches on at some finite proper time). In other words, we are not in the Unruh vacuum.

Now, of course there is going to be a blue shift for noninertial observers, which they compute explicitly (and looks correct to me, as I've seen similar expressions albeit with less generality in eg Wald and other papers).

There is a bit of a funny claim/calculation very close to horizon crossing, and I'm not sure I agree with the paper on that point. The real issue is how far you can trust quantum field theory in curved spacetime past a certain limit. Here we are dealing with modes that diverge as something like e^k(u)T, so a detector with a finite response frequency v will have to resolve trans Planckian modes for T > 1/K(u). The authors are evidently aware of this point, as its related to their discussion on the validity of the adiabatic limit.

But anyway, I don't think this paper really challenges anything about the standard lore (except perhaps for worldlines that are very/very close to the horizon, where there is a claimed jump in the Unruh temperature) but this doesn't really run against the equivalence principle in any way.

edit: Thinking about this a bit more, I'm convinced the paper is correct, however a near horizon observer is not really measuring what I would call the Hawking effect perse. Instead he/she is just measuring a perfectly classical effect of a time varying gravitational field, NOT the subtle features of the quantum vacuum that traditionally gives rise to the Hawking effect. Analysis of that point, really requires putting in a detector (along with the deep subleties about quantum measurement in curved space) and carefully subtracting off the classical effects.

 

[tionis]

however a near horizon observer is not really measuring what I would call the Hawking effect perse. Instead he/she is just measuring a perfectly classical effect of a time varying gravitational field, NOT the subtle features of the quantum vacuum that traditionally gives rise to the Hawking effect. Analysis of that point, really requires putting in a detector (along with the deep subleties about quantum measurement in curved space) and carefully subtracting off the classical effects.

From the author...

Dear Haelfix: The vacuum of the quantum field gets altered due to the presence of horizon structure in the spacetime. It is like changing the boundary conditions. The observer who is falling in sees two effects one due to time varying gravitational field as he falls and the spacetime has horizon structure. Both of these alter the quantum vacuum and hence give rise to radiation. The effects cannot be resolved as such but one can show for example that the temperature seen by a freely falling observer from far off when he is near the horizon is 4 times the usual hawking temperature seen by the observer who is at rest very far away from the black hole.