BH can't evaporate in real surroundings (George Ellis)

[marcus]

Common sense really. Space is full of CBR (not to mention other radiation and matter). They keep being fed. The surrounding CBR is warmer than the Hawking temperature of the hole and in effect blocks the Hawking radiation process. Ellis et al even calculate far into the future when the CBR is much cooler---even then given the positive constant Lambda of the standard cosmic model they find the BH is unable to completely evaporatehttp://inspirehep.net/record/1306275
Astrophysical Black Hole horizons in a cosmological context: Nature and possible consequences on Hawking Radiation
George F R Ellis, Rituparno Goswami, Aymen I. M. Hamid, Sunil D. Maharaj
This paper considers the nature of apparent horizons for astrophysical black hole situated in a realistic cosmological context. Using semi-tetrad covariant methods we study the local evolutions of the boundaries of the trapped region in the spacetime. For a collapsing massive star immersed in a cosmology with Cosmic Background Radiation (CBR), we show that the initial 2 dimensional marginally trapped surface bifurcates into inner and outer horizons. The inner horizon is timelike while the continuous CBR influx into the black hole makes the outer horizon spacelike. We discuss the possible consequences of these features for Hawking radiation in realistic astrophysical contexts.
13 pages, 4 figures, Jul 14, 2014 http://arxiv.org/abs/1407.3577

This has consequences for the expected prevalence of primordial BH explosions according to a followup paper:

http://inspirehep.net/record/1309567
Cosmic Matter Flux May Turn Hawking Radiation Off
Javad T. Firouzjaee, George F. R. Ellis
(Submitted on 4 Aug 2014)
An astrophysical (cosmological) black hole forming in a cosmological context will be subject to a flux of infalling matter and radiation, which will cause the outer apparent horizon (a marginal trapping surface) to be spacelike [5]. As a consequence the radiation emitted close to the apparent horizon no longer arrives at infinity with a diverging redshift. Standard calculations of the emission of Hawking radiation then indicate that no blackbody radiation is emitted to infinity by the black hole in these circumstances, hence there will also then be no black hole evaporation process due to emission of such radiation as long as the matter flux is significant. The essential adiabatic condition (eikonal approximation) for black hole radiation gives a strong limit to the black holes that can emit Hawking radiation. We give the mass range for the black holes that can radiate, according to their cosmological redshift, for the special case of the cosmic blackbody radiation (CBR) influx (which exists everywhere in the universe). At a very late stage of black hole formation when the CBR influx decays away, the black hole horizon becomes first a slowly evolving horizon and then an isolated horizon; at that stage, black hole radiation will start. This study suggests that the primordial black hole evaporation scenario should be revised to take these considerations into account.
21 pages, 6 figures, http://arxiv.org/abs/1408.0778

==quote Ellis and Firouzjaaee, conclusions==
• Application of this constraint to primordial black hole evaporation modeling may bring in a correction to their abundance in the cosmos. Specifically, primordial black holes are candidate progenitors of unidentified Gamma-Ray Bursts (GRBs) that are supposed to detect by the Fermi Gamma-ray Space Telescope observatory. Their abundance might be lowered when the above considerations are taken into account.
This is all in accord with the discussions in [5, 10], and leads to the conclusion that in a realistic cosmological context, a black hole forming from the collapse of a star in a universe permeated by CBR and matter will not emit Hawking radiation in the past or at the present, and so emission of such radiation from them, or evaporation of such black holes in an explosion, will not occur in the visible universe. To what degree this affects primordial black holes will be very context dependent and will need detailed modeling.
==endquote==

In one sense it should make PBH MORE ABUNDANT because some of the small ones which WOULD have already evaporated will have been fed enough to survive.
But it is not clear whether it would make visible GRB more or less abundant. The population of PBH might be larger but fewer might be exploding in our neighborhood.
According to the Hawking model, you don't get an explosion until the BH has evaporated down to nearly nothing. there is a bright flash at the very end.

This Ellis et al paper would have different implications for the Planck star model. It will be interesting to see if any revised expectations come out of it. In the Planck star BH model the lifespan is much shorter. The GRB is much brighter (so more likely to be visible) and it occurs when the BH has only gone through a third or so of its Hawking lifetime. The bounce explosion s not determined by the BH evaporating down to some critical size, it is determined by a time-dilated rebound which proceeds on its own schedule.

 

[mfb]

even then given the positive constant Lambda of the standard cosmic model they find the BH is unable to completely evaporate

Looks like this is model-dependent. From the second paper:

However, leaving aside strange behaviour such as dynamical dark energy, cosmological particle
creation, and big crunch singularity models, this picture says that at very large times there is effectively
no CBR flux. Although it never becomes exactly null or timelike ([5], section VIII.2), the OMOTS
eventually becomes an isolated horizon that is very close to the classical event horizon. Hawking
Radiation emission could occur from that time on as depicted in Fig.(5), because the approximations we
have used above in the eikonal analysis would break down at that stage, with associated backreaction
effects and possibly eventual black hole evaporation.

This is the key difference from the particle approximation and associated tunneling picture, because
on that view, there would never be Hawking radiation emission, as the OMOTS surface would always be
spacelike, so no Hawking Radiation backreaction effects or black hole evaporation would occur even in
the very far future

 

[marcus]

Thanks for comment, Mfb, yes, let's be clear!
They say unequivocally that astrophysical BH do not evaporate. The emission of Hawking radiation is currently being prevented.
The mere presence of the CBR is, by their analysis, sufficient to prevent evaporation (i.e. the emission of Hawking radiation)

However in the far future, say 100 billion years from now or a trillion years from now, when the CBR is much colder (due to expansion) they allow that BH MAY (or may not) begin to evaporate.
What happens in very distant future is, as you say, "model dependent".

BH may begin to evaporate by emitting Hawking radiation, and they may or may not carry that all the way to a complete evaporation. As I recall the authors explore several possible asymptotic outcomes in the very long term. But as I recall they leave the very long term stuff unresolved. Those are questions to be answered by future research if they can be answered at all.

 

[marcus]

What interests me especially about the Ellis Firouzjaee paper is how it affects the phenomenology of primordial black holes (PBH) and the Planck star model of black hole.

According to the Planck star model a BH collapse undergoes a bounce resulting in a brief GRB (gammaray burst) explosion. The bounce is time-dilated by the intense gravity at collapse center. So to an outside observer the GRB does not appear until long afterwards. However this does not allow time for much Hawking radiation to occur at the temporary horizon. If Hawking evaporation does occur at all, it does not have time to dissipate more than a third or so of the initial mass, before the final explosion ends the collapse process.

The Planck star (PS) model has a clearly distinct phenomenology as regards primordial BH. If PBH formed in the early universe then according to PS model more of them should be ready to explode, and the explosions should be brighter, than would otherwise be expected. So orbital gammaray instruments should be detecting very brief small explosions in our galaxy.

This is clearly different from what the conventional Hawking scenario would say because in that scenario all evaporations end in the same small flash when the mass finally dwindles down to some tiny terminal amount. The resulting small flashes would only be detectable if they were in the immediate vicinity of the solar system.

The PS model allows for brighter flashes and thus for more of them to be detected. Also the absolute magnitude and characteristic gamma wavelengths should be predictable because one should be able to calculate the initial mass range of PBH which are currently ripe to explode. The extent of time dilation (of the bounce) must depend on the initial mass.

So these differences make the PS model testable. And what I'm wondering is how the phenomenology is affected by the in falling matter/radiation considerations raised by Ellis Firouzjaee

 

[Haelfix]

I don't think very much. The much larger systematic uncertainty relates to the cross section of primordial black holes to begin with.

As it stands there is no accepted mechanism for their formation in the early universe. The models that do exist, are extremely sensitive to initial conditions/departures from homogeneity/the form of the shock fronts, etc, and in general the abundance is also very sensitive to how inflation proceeds.

Since we don't know the initial conditions of the early universe, the mechanism by which primordial black holes are formed, how many efolds of inflation the universe undergoes, much less the actual geometries that need to be considered (the Ellis paper shows how much timeframes can parametrically change by considering even small departures from stationarity) any estimate of the cross section of pbh will have very large theoretical uncertainties.. Much, much larger than any model dependant considerations about the actual evaporation process.

So even if very specific gamma ray signatures are seen and isolated from the already very dirty astrophysics error bars, it will be extremely difficult phenomenologically to untangle the actual physics given the uncertainties in abundance.

Keep in mind, even the Ellis paper is extremely naive in how they estimate time frames. Real astrophysical black holes in addition to the usual greybody factors, necessitate precise estimates on how galaxies evolve over time. The matter flux will be an extremely complicated function of time, and its just a mess all around to try to predict exact figures.

 

[tzimie]

If BH can't evaporate, doesn't it solve the information paradox?

 

[marcus]

If BH can't evaporate, doesn't it solve the information paradox?

I'd say yes. Ellis' paper allows for the BH eventually beginning to evaporate, however. I'm not sure the eventual question is resolved.

Ellis' paper is on a separate line of investigation from the Planck star papers of people like Rovelli, Vidotto, Haggard, and Barrau. Their idea is that for a substantial part of its lifetime the BH behaves outwardly just like a conventional BH. So if Ellis' paper is wrong and Hawking radiation is not shut off by the environment, then the nonsingular BH (Planck star model) would radiate just like the conventional model would.

I haven't heard Rovelli or his collaborators address the issue raised in Ellis' paper. I presume that if Ellis is right and Hawking radiation has so far been shut down then that would carry over to their nonsingular BH version.
If according to the usual ILQGS format, the slides PDF and audio for Rovelli's October 14 Planck star talk will be:
http://relativity.phys.lsu.edu/ilqgs/rovelli101414.pdf
http://relativity.phys.lsu.edu/ilqgs/rovelli101414.wav

Whatever turns out to be the case with the Ellis' suggestion that Hawking radiation is shut off (at least until the far distant future when CBR is cooled way down) the Planck star model is explicitly claimed to resolve info paradox (and to be to some extent observationally testable).

The Planck star explodes as GRB while it still has most of its mass, so it can deliver up the information it has temporarily sequestered. Resolving the information paradox is a major issue so I'm certain that Rovelli will touch on that point in his Oct 14 online ILQGS talk.