Black holes in AsymSafe gravity (new Easson paper)

[marcus]

http://arxiv.org/abs/1007.1317
Black holes in an asymptotically safe gravity theory with higher derivatives
Yi-Fu Cai, Damien A. Easson
22 pages, 3 figures
(Submitted on 8 Jul 2010)
"We present a class of spherically symmetric vacuum solutions to an asymptotically safe theory of gravity containing high-derivative terms. We find quantum corrected Schwarzschild-(anti)-de Sitter solutions with running gravitational coupling parameters. The evolution of the couplings is determined by their corresponding renormalization group flow equations. These black holes exhibit properties of a classical Schwarzschild solution at large length scales. At the center, the metric factor remains smooth but the curvature singularity, while softened by the quantum corrections, persists. The solutions have an outer event horizon and an inner Cauchy horizon which equate when the physical mass decreases to a critical value. Super-extremal solutions with masses below the critical value correspond to naked singularities. The Hawking temperature of the black hole vanishes when the physical mass reaches the critical value. Hence, the black holes in the asymptotically safe gravitational theory never completely evaporate. For appropriate values of the parameters such stable black hole remnants make excellent dark matter candidates."

Earlier this year Easson co-authored a couple of cosmology papers with Nobel laureate George Smoot. He and Cai have some interesting things to say here.

One helpful extra feature of the paper is that it gives a concise summary of the present situation in A.S. research. We have been following AS here at PF Beyond forum since 2006 or so. It has come a long way since then and it's nice to have a fresh perspective overview from someone like Easson who is new to it.

 

[marcus]

Here is an excerpt from the Introduction on page 2 of the Cai Easson paper:

One of the most challenging tasks facing theoretical physicists today is the construction of a consistent ultraviolet (UV) complete theory of gravity. Weinberg has suggested that the effective quantum field description of a gravitation theory may be UV complete and non-perturbatively renormalizable by virtue of asymptotic safety (AS) [1]. In this scenario the renormalization group (RG) flows have a fixed point in the UV limit and a finite dimensional critical surface of trajectories approach this point at short distances. This theory has been extensively studied in the literature [2–9], and recent evidence suggests the UV critical surface is only three-dimensional even in truncations of the exact RG equations with more than three independent coupling parameters [10–15]. Until now, the majority of the work on the subject has considered significant truncations of the action, taking into account only the Einstein-Hilbert and occasionally cosmological constant terms. In this paper, we initiate the study of black hole solutions in an asymptotically safe gravity theory including higher derivative terms and running gravitational couplings...

We've discussed some of this. Weinberg's July 2009 talk at CERN where he pointed out to the many string theorists in the audience that string might not be needed and might not be "how the world is" because of asymptotic safety (his original idea back in 1976). UV complete gravity + "good old" QFT, as he put it. His own research at that point was using AsymSafety to explain cosmological inflation without needing some exotic inflaton field---just by the running of couplings.*

Now Cai Easson seem to be trying to explain dark matter using running couplings, without needing to invoke some exotic new particle. It seems like an ambitious and risky proposal, but they claim it is testable.

FWIW I still lean towards thinking of dark matter as some particle, which will in due time be determined, but why reject Cai Easson's idea as long as what they say is right about it's being testable?

In any case somebody had to initiate the study of black holes under the assumption of AsymSafe gravity.

*If anyone wants links to the video of Weinberg's July 2009 CERN talk and his recent paper on cosmology with asymsafe gravity, please say. They are easy to find but I'd be glad to fetch them.

 

[JustinLevy]

I do not consider this boding well for the Asymptoticly Safe gravity approach. The exact opposite actually.

If correct, the paper shows that even if there is a fixed point in the theory, this form of quantum gravity predicts its own downfall. It leads to situations which can evolve to containing an actual singularity, and therefore the theory can't predict how it evolves. These singularities of classical gravity are something a true quantum gravity theory must avoid to maintain the ability for the theory to predict evolution.

Additionally, it leads to Cauchy horizons which a particle can hit, and by definition then the theory cannot describe how the evolution continues. Evaporation from such a black hole cannot be unitary. The theory leads to predictions countering its own starting point (unitary evolution in quantum mechanics). This is the old "information paradox" we expect a true quantum gravity theory to fix.

If this paper is correct, it shows that being "asymptotically safe" is not enough.

 

[marcus]

Those are good points! We'll see how the established experts in AS gravity respond.
There are a bunch of them now: Percacci, Reuter, Saueressig, Benedetti, Bonanno,...
and of course Steven Weinberg. :-D Easson is kind of a new kid on the block. Just have to see.

 

[atyy]

Try the discussion in section D "Absence of curvature singularities" in http://arxiv.org/abs/1002.0260

But unitarity might be a problem anyway, or not.

"Q: If gravity is asymptotically safe, almost certainly it will contain higher derivative terms. Is this not going to spoil unitary? We do not know. Just note that knowledge of the FP action is not enough to decide." http://www.percacci.it/roberto/physics/as/faq.html

An interesting recent critique of asymptotic safety comes from http://arxiv.org/abs/1006.0984

 

[MTd2]

These singularities of classical gravity are something a true quantum gravity theory must avoid to maintain the ability for the theory to predict evolution.

Hmm, it seem that the solution they found is actually coherent to the initial proposition of Asymptotic safety, which is to find an attractor point which makes scattering finite. If you hide always behind an horizon the source of divergence, there is no more problem for the rest of the universe.

And there is a final state, which is a black hole of finite mass.

What sounds bad to me it is that why not the whole universe has not coalesced into these black holes? Diverging singularities should melt particles at black holes at every interaction so that the only observable state would be the critical black hole. Right?

 

[Finbar]

Hmm, it seem that the solution they found is actually coherent to the initial proposition of Asymptotic safety, which is to find an attractor point which makes scattering finite. If you hide always behind an horizon the source of divergence, there is no more problem for the rest of the universe.

And there is a final state, which is a black hole of finite mass.

What sounds bad to me it is that why not the whole universe has not coalesced into these black holes? Diverging singularities should melt particles at black holes at every interaction so that the only observable state would be the critical black hole. Right?

your only going to create black holes with energies k>M_pl.
Others wise gravity is too weak.

 

[MTd2]

Where is written that there is a minimum mass for black holes in AS?

 

[marcus]

Where is written that there is a minimum mass for black holes in AS?

Atyy reminded us of this February 2010 paper which was added to the bibliography thread here:
https://www.physicsforums.com/showthread.php?p=2559015#post2559015
I had forgotten about it. Daniel Litim has been doing AS research for several years and has held a conference at Sussex, where it was one of the main focuses. He delivered an AS talk at the 2009 Planck Scale conference. He is not a "newcomer" to AS, more of an "old hand."
It's good to know that Litim has contributed an AS paper on black holes:
http://arxiv.org/abs/1002.0260
Black holes and asymptotically safe gravity
Kevin Falls, Daniel F. Litim, Aarti Raghuraman
(Submitted on 1 Feb 2010)
"Quantum gravitational corrections to black holes are studied in four and higher dimensions using a renormalisation group improvement of the metric. The quantum effects are worked out in detail for asymptotically safe gravity, where the short distance physics is characterized by a non-trivial fixed point of the gravitational coupling. We find that a weakening of gravity implies a decrease of the event horizon, and the existence of a Planck-size black hole remnant with vanishing temperature and vanishing heat capacity. The absence of curvature singularities is generic and discussed together with the conformal structure and the Penrose diagram of asymptotically safe black holes. The production cross section of mini-black holes in energetic particle collisions, such as those at the Large Hadron Collider, is analysed within low-scale quantum gravity models. Quantum gravity corrections imply that cross sections display a threshold, are suppressed in the Planckian, and reproduce the semi-classical result in the deep trans-Planckian region. Further implications are discussed."
Comments: 21 pages, 9 figures

At the moment I'm unsure what to think. If I understand correctly, Easson claims that including higher derivative terms reverses some of the Litim et al findings.
MTd2 I think you will find something about a minimal BH size in the Litim paper.
Thanks to Atyy for reminding us of this paper, which had slipped my mind.

your only going to create black holes with energies k>M_pl.
Others wise gravity is too weak.

Finbar! good to see you on this thread. I suspect you might have a general argument for Planck mass being minimal BH mass, because of general assumptions about Planck length, Compton wavelength etc. though I'm not sure what you have in mind. Or whether it would apply if one is trying to work entirely in the context of AS gravity. Do you have an argument that only depends on the AsymSafe gravity framework, showing that the minimal size BH is Planck?
Maybe you can help me (us?) with our reading of the Easson and Litim papers.

 

[Finbar]

Where is written that there is a minimum mass for black holes in AS?

Did you read the paper? Or any of the other papers on AS black holes?

The conclusions of this paper are the same as those of Reuter and Bonanno's original paper

http://arxiv.org/abs/hep-th/0002196

and the higher dimensional solutions of Litim etc.

There is a smallest black hole with a vanishing temperature.

 

[MTd2]

The paper in question for this thread talks about a naked singularity below Mc.Naked singularities sounds like a kind of black hole to me.

 

[Finbar]

The paper in question for this thread talks about a naked singularity below Mc.Naked singularities sounds like a kind of black hole to me.

If there's no event horizon (or even a trapping surface) its not a black hole by definition.
Signals can be sent from any point to spatial infinity.

Note also that a black hole of mass M cannot evolve into a state M<M_c, via hawking radiation, since the temperature falls to zero at M=M_c. So you won't get a naked singularity.

 

[MTd2]

But my observation was about forming a naked singularity directly.

 

[Finbar]

But my observation was about forming a naked singularity directly.

Well research hasn't been done into whether or not it is likely that these can be formed or not.
There is no singularity theorem for the forming of such a naked singularity.

But you make a good point this issue does need to be understood. But my guess is that at energies M<M_c gravity is too weak to form these singularities.

 

[MTd2]

It would be too weak if they were like 1/r, and so could be removed like a log divergence. But at the vicinity of Mc, they seem to have a -1.5 divergence, so it seems like there would be still an annoying interval until the gravity is weak enough.

 

[atyy]

It would be too weak if they were like 1/r, and so could be removed like a log divergence. But at the vicinity of Mc, they seem to have a -1.5 divergence, so it seems like there would be still an annoying interval until the gravity is weak enough.

Falls et al have singularities depending on what matching condition and sigma are used - any idea what that is about?

 

[MTd2]

Hmm. I really have no idea.

 

[atyy]

Hmm. I really have no idea.

Me too.

Cai and Easson talk about the discrpenency between their results and Falls's: "We note that this relation is different from the result p ~ r−3/2 appearing in [27] through a UV matching. The discrepancy is due to the action truncation considered in [27], which consisted of only the Einstein-Hilbert term and a vanishing cosmological constant. In the present analysis, we include the higher derivative terms and nonzero cosmological constant in addition to the EH term and running GN. Consequently, we consider the effective action in the low energy limit. When the momentum cutoff flows to the IR regime, the high-derivative terms are suppressed automatically and thus becomes negligible. In this case, p ~ 1/r which is consistent with the IR matching of [27]."

I guess all these different truncations of the full action are questionable. I remember Distler had some problem with this too, and Benedetti et al http://arxiv.org/abs/0902.4630 had some reply, at least for the particular terms Distler brought up, but maybe not necessarily for all terms that in principle do appear?

Incidentally, Magnen et al http://arxiv.org/abs/0906.5477 also had a complaint about this in a footnote "Obviously, this is not the case in the asymptotic safety scenario. The recourse to uncontrolled truncations of the effective action, however, makes this program difficult to justify from a mathematical physics perspective." But I wasn't sure how seriously to take it, since historically one often has had to start unrigourously in physics.

The thing that makes me less enthusiastic about AS these days is that the computational result from CDT in lower dimensions now seems to diverge from AS http://arxiv.org/abs/0911.0401 . (Actually I'm not sure I've read that correctly. Is it CDT != AS in D<4, and CDT ~ Horava ?)

 

[MTd2]

I am not sure if the problem is the truncation of the theory, but It seems strange,even wrong, that a classical solution, ansatz, was found and then see how it would be modified by a truncation, in the strong limit region.

 

[Finbar]

Using a truncation is an approximation. Just as doing a 2 loop calculation is an approximation.
At the moment there is evidence for AS within this approximation scheme. It's not a proof but the results are very encouraging.

The issue with the scale matching p ~ r^-(gamma) is a subtle issue but its more to do with how one goes from momentum to position space in curved space time. The naive thing to do is say p ~ 1/r this should hold when spacetime is approximately flat i.e. in the IR. In Litim's paper they introduce the parameter gamma and note that for gamma= (d-1)/(d-2) in the UV you get a deSitter core in all d.

Easson's paper seems to offer a more general way of obtaining the matching in the UV.