Do Black Holes become visible at relativistic speeds?

[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.