Dave Mattingly has been a frequent collaborator with Ted Jacobson (his thesis advisor). You know of Jacobson if, for example, you followed the recent discussion of "gravity as entropic force" by Erik Verlinde and others. In 1995 Jacobson derived the Einstein field equation from thermodynamics. Or if you followed the Perimeter conference last year on Horava gravity (where J. led the concluding discussion.) Or if you watched the Santa Barbara KITP workshop on quantum spacetime singularities (to a large extent about black holes). Jacobson has QG cred, and some of that rubs off. Mattingly is comparatively young but it's probably worthwhile seeing what he has to say about Asymptotic Safety. So here's this recent paper.(adsbygoogle = window.adsbygoogle || []).push({});

http://arxiv.org/abs/1006.0718

Asymptotic Safety, Asymptotic Darkness, and the hoop conjecture in the extreme UV

Sayandeb Basu, David Mattingly

9 pages

(Submitted on 3 Jun 2010)

"Assuming the hoop conjecture in classical general relativity and quantum mechanics, any observer who attempts to perform an experiment in an arbitrarily small region will be stymied by the formation of a black hole within the spatial domain of the experiment. This behavior is often invoked in arguments for a fundamental minimum length.Extending a proof of the hoop conjecture for spherical symmetry to include higher curvature terms we investigate this minimum length argument when the gravitational couplings run with energy in the manner predicted by asymptotically safe gravity. We show that argument for the mandatory formation of a black hole within the domain of an experiment fails. Neither is there a proof that a black hole doesn't form. Instead, whether or not an observer can perform measurements in arbitrarily small regions depends on the specific numerical values of the couplings near the UV fixed point. We further argue that when an experiment is localized on a scale much smaller than the Planck length, at least one enshrouding horizon must form outside the domain of the experiment. This implies that while an observer may still be able to perform local experiments, communicating any information out to infinity is prevented by a large horizon surrounding it, and thus compatibility with general relativity can still be restored in the infrared limit."

One thing is he knows the recent AS literature, for example citing not just an old review paper by Martin Reuter but also imporatnt new work like the 2010 paper of Benedetti, Machado, Saueressig. He knows how the Newton's constant runs in recent AS treatments.

The dimensionful coupling, Newton's constant, goes to zero, as the energy scale increases. It turns out to be crucial how the dimensionless version g = G_{N}(p)p^{2}behaves in the UV limit. Benedetti et al found the asymptotic value was around g_{*}= 2.

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# Asymptotic safety and black holes (new Mattingly paper)

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