Stability of Minkowski and deSitter Spaces in GR

[marcus]

Minkowski space and deSitter space have been shown to be stable in GR under small perturbations. Perturbations do not intensify in higher frequency modes--these solutions don't go haywire and develop black holes all over the place.

Piotr Bizon has shown that Anti-deSitter (AdS) space is not stable.
http://inspirehep.net/search?p=find+eprint+1104.3702
This has naturally attracted a lot of attention and Bizon will be giving a plenary talk about it at the GR20 conference at Warsaw in about 3 weeks.
http://gr20-amaldi10.edu.pl/index.php?id=29
To show context, here is a sampling of the scheduled plenary talks:

Monday 8 July
...
Last 60 years of GRG: From the GR3 to GR 20 Warsaw conferences
Abhay Ashtekar, Penn State University, USA
The 1962 GR3 conference in Warsaw/Jablona was a milestone in that, thanks to participants like Bergmann, Bondi, Chandrasekhar, DeWitt, Dirac, Ehlers, Feynman, Infeld, Lichnerowicz, Synge, Weber and Wheeler, it sparked new directions of research in mathematical GR, gravitational waves, quantum gravity and relativistic astrophysics. Our field has evolved tremendously since then. I will illustrate these advances by contrasting what was discussed then and what we know now.

Loop Quantum Gravity (LQG)
Thomas Thiemann, University of Erlangen-Nurnberg, Germany
Loop Quantum Gravity (LQG) is a specific realisation of a Quantum Field Theory of General Relativity including matter based on the canonical approach. In this talk we summarise the current status of LQG. Emphasis will be laid on the physical motivation for and mathematical foundations of the theory as well as recent developments.

Status of Advanced (Ground Based) Gravitational Wave Detectors
M. Evans MKI, M.I.T, USA
...I'll briefly introduce the technological challenges involved in 2nd generation ground based detectors, and then move on to the status of the projects that are currently underway.

Neutron Stars
James Lattimer, Stony Brook University, USA
Neutron stars are laboratories for dense matter and gravitational physics. ... setting bounds to neutron star masses, radii, rotation rates, temperatures and ages.

Tuesday 9 July
A Galactic Scale Gravitational Wave Observatory
Maura McLaughlin, West Virginia University, USA
Timing an array of pulsars could result in the detection of a stochastic gravitational wave background, most likely resulting from an ensemble of supermassive black hole binaries, ...

Numerical relativity: The role of black holes in gravitational wave physics, astrophysics and high-energy physics
Ulrich Sperhake, DAMTP, University of Cambridge, UK
We review the latest advances in the numerical simulation of black hole dynamics in the framework of general relativity and alternative theories of gravity...
...

Wednesday 10 July
Black hole microstate counting and their macroscopic counterpart
Ashoke Sen, Harishchandra Research Institute, India
We survey recent results on the exact counting of the microstates of a class of supersymmetric black holes in string theory,...
...
Entanglement Entropy and Gravity/Condensed Matter Correspondence
Tadashi Takayanagi , YITP, Kyoto University, Japan
The entanglement entropy has been very important in various subjects such as the quantum information theory, condensed matter physics and quantum gravity...
...
Resolving Black Holes with the Event Horizon Telescope
Avery Broderick, Perimeter Institute, Canada
Supermassive black holes reside at the centers of most, if not all, galaxies ... However, due to their compact nature, it remains unclear how they grow, launch relativistic outflows, and even if event horizons exist. These questions are now being answered by an unprecedented capability to resolve structure ..., an Earth-sized array of millimeter-wave observatories, and how ... observations are already providing novel insights...

Thursday 11 July
Planck results and consequences for Cosmology
Georges Efstathiou, University of Cambridge, UK

Is AdS stable?
Piotr Bizoń, Uniwersytet Jagielloński, Poland
The short answer is: most likely not. A longer answer, to be presented in the talk, will include recent numerical, physical, and mathematical evidence which indicates that the AdS space is unstable.
...
...
Friday 12 July
Observational Results from Ground-based Gravitational Wave Detectors
Marie Anne Bizouard, LAL Orsay, France & Carleton college USA
...

Experimental Gravitation with Cold Atoms
Peter Wolf, SYRTE, Observatoire de Paris, France
... Over the last decades precision metrology has moved away from “classical” methods towards quantum phenomena, in particular those of atomic physics,...
I will give a (necessarily non-exhaustive) overview of recent and near future experiments in gravitation that are based on atomic physics, and more precisely on sensors using laser cooled atoms for ultimate precision. ...

Present and future cosmological constraints on Dark Energy
Tamara Davis, University of Queensland, Australia
... Every measurement made so far remains consistent with dark energy being a cosmological constant, or vacuum energy. ...
In this talk I will review the many varied observations that now confirm dark energy, why we trust them, where their weaknesses lie, and show the points of slight conflict that are appearing. I will also review upcoming projects that should provide different types of cosmological information that will help distinguish between different theoretical explanations for dark energy.
=====end of plenary talks schedule======

 

[marcus]

Here's the main paper:
http://arxiv.org/abs/arXiv:1104.3702 (53 cites)
On weakly turbulent instability of anti-de Sitter space
Piotr Bizoń, Andrzej Rostworowski
(Submitted on 19 Apr 2011)
We study the nonlinear evolution of a weakly perturbed anti-de Sitter (AdS) spacetime by solving numerically the four-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant. Our results suggest that AdS spacetime is unstable under arbitrarily small generic perturbations. We conjecture that this instability is triggered by a resonant mode mixing which gives rise to diffusion of energy from low to high frequencies.
4 pages, 4 figures. Published in Physical Review Letters (2011)

Numerical GR is Bizon's main specialty
http://inspirehep.net/author/P.Bizon.1/
Here is a follow-up paper extending the result to higher dimensions:

http://arxiv.org/abs/arXiv:1108.4539 (24 cites)
A comment on AdS collapse of a scalar field in higher dimensions
Joanna Jałmużna, Andrzej Rostworowski, Piotr Bizoń
(Submitted on 23 Aug 2011)
We point out that the weakly turbulent instability of anti-de Sitter space, recently found in arXiv:1104.3702 for four dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant, is present in all dimensions d+1 for d ≥ 3, contrary to a claim made in arXiv:1106.2339.
3 pages, 2 figures. Published in Physical Revew D (2011)

 

[arivero]

Hmm usually AdS was stabilized somehow by the tensor $A_{NMP}$ of 84 components that happens to be the complement of the D=11 graviton. Not other dimension works, and you really need this tensor.

 

[yenchin]

While AdS seems to be unstable, many asymptotically AdS spacetimes seem to be stable:
http://arxiv.org/abs/1208.5772.

It also seems that, flat space inside a cavity is likewise unstable: http://arxiv.org/abs/1208.2934.

 

[marcus]

While AdS seems to be unstable, many asymptotically AdS spacetimes seem to be stable:
http://arxiv.org/abs/1208.5772.
...

The authors (Don Marolf, Gary Horowitz et al) make Bizon's paper that I linked their reference [1].
They confirm Bizon's result about AdS unstable, and give some extra understanding!

I would recommend looking at both
the Bizon original arXiv:1104.3702
and theirs arXiv:1108.5772

You get a better intuitive feel for WHY AdS is unstable, by reading the KITP Santa Barbara authors. Smart reputable people, who take the instability seriously, and their analysis of a few special asympt. AdS cases does not, I think, make the problem go away.

 

[arivero]

Freund Rubin spaces?

 

[yenchin]

Freund Rubin spaces?

Are you asking if the said instability of AdS extends also to AdS x compactified space, like $AdS_5 \times S^5$?

 

[arivero]

Are you asking if the said instability of AdS extends also to AdS x compactified space, like $AdS_5 \times S^5$?

More or less. I was thinking $AdS_4 \times M^7$, which is the original Freund-Rubin case.

 

[yenchin]

That's an interesting question, I would love to know the answer too

 

[mitchell porter]

I am still trying to get a handle on this, but I'll just mention two obvious questions:

Does this instability persist in the quantum theory of AdS?

What does it correspond to, in the dual CFT?

 

[atyy]

I am still trying to get a handle on this, but I'll just mention two obvious questions:

Does this instability persist in the quantum theory of AdS?

What does it correspond to, in the dual CFT?

The paper that yenchin linked to says "It has long been known that anti-de Sitter (AdS) spacetime is stable to linearized perturbations, and positive energy theorems ensure that AdS cannot decay. However, there is growing evidence that AdS is nonlinearly unstable, in the sense that any finite perturbation will eventually become large and, at least in many cases, form a small black hole [1, 2, 3]." Their first reference is the Bizon and Rostworowski paper in marcus's OP.

I usually associate black hole formation with something like thermalization, so perhaps that would be the process in the dual CFT? Maybe like in http://www.phy.duke.edu/~muller/Talks/QM2011.pdf ?

 

[marcus]

Does this instability persist in the quantum theory of AdS?

What does it correspond to, in the dual CFT?

==quote http://arxiv.org/pdf/1109.1825v1.pdf conclusions page 4==
Our discussion so far has been entirely classical. Quantum mechanically, we expect that the transfer of energy from large to small scales will still occur, but now will be cut off at a frequency equal to the initial energy. So if one starts with an initial state consisting of a large number of low energy quanta with total energy less than the Planck energy, one will never form a black hole.
==endquote==

Planck energy is not much in cosmic terms (only a few hundred kilowatt-hours). So generally speaking, limiting total energy to E_planck is not a very effective way to ensure stability in the quantum case. In effect, they suggest that the answer to your question is yes: the instability persists in the quantum theory.

They also discuss what the instability corresponds to in the dual CFT.

==quote Gary Horowitz and friends, conclusions page 4==
We now comment on the dual field theory interpretation of our results using gauge/gravity duality. Since we have only considered gravity in the bulk, any field theory with a gravity dual must exhibit the same turbulent instability, and transfer energy from large to small scales. The fact that this is so universal seems surprising, although the final outcome of a small black hole can be viewed as thermalization in a microcanonical ensemble. It is even more surprising considering the fact that our dual system is 2 + 1 dimensional, and in this case classical turbulence causes energy to flow from small to large scales [13]. Our results indicate that (at least at large N ) strongly coupled 2 + 1 dimensional quantum theories in finite volume behave very differently. We have found similar results in AdS₅, ...
...
We have argued that asymptotically AdS solutions are generically singular. It would be of great interest to prove a singularity theorem establishing this rigorously.
==end of article==