What says Reuter re black holes?

[marcus]

Reuter (and co) have given a "new look" to Quantum Gravity.
There is mounting evidence that gravity is renormalizable
and indeed that Reuter and company have, by finding the fixed point, renormalized it.

So what does Reuter say about black holes?

Anybody know? Anybody want to comment?

 

[marcus]

As I recall it, Reuter finds that as the proximity scale k goes to infinity
G --> 0
Lambda --> infty

which would mean that, at the very pit of black hole collapse, gravity becomes repellant.

IOW at very high densities where everythng is extremely close together (the high k regime) the "dark energy" expansive effect of the cosmological constant Lambda becomes dominant----so that apparently a singularity cannot occur.

Intuitively, one would say there should be a bounce.

Just my naive two cents. Does anyone here who has chatted with Reuter in person know his views on black hole?

 

[jal]

Maybe the answer can be deducted from the following paper
Here is what Reuter has to say about 2d.
http://arxiv.org/abs/hep-th/0508202
Fractal Spacetime Structure in Asymptotically Safe Gravity
Authors: O. Lauscher, M. Reuter
(Submitted on 26 Aug 2005)
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton's constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. Contact is made with recent Monte Carlo simulations.
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Are we to deduct that small black holes are 2d and that large black holes are 4d?

 

[marcus]

Maybe the answer can be deducted from the following paper
Here is what Reuter has to say about 2d.
http://arxiv.org/abs/hep-th/0508202
Fractal Spacetime Structure in Asymptotically Safe Gravity
Authors: O. Lauscher, M. Reuter
(Submitted on 26 Aug 2005)
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton's constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. Contact is made with recent Monte Carlo simulations.
---------------
Are we to deduce that small black holes are 2d and that large black holes are 4d?

Thanks for bringing this paper up. It is a good find: one of the most interesting QG papers I know of. We had a brief discussion of it here at PF back in 2005 in connection with the Causal Dynamical Triangulations paper on spectral dimension that got a similar result---that was Ambjorn Jurkiewicz and Loll. We hardly gave this paper the attention it deserves.

I can't answer your question. The transition to 2D is SMALLER THAN PLANCK SCALE. I'm not sure one can have a solution of General Relativity containing black holes that small. the compton wavelength (the indefiniteness of position) would be bigger than the schwarzsch. radius.

for a black hole to be small enough that it could live entirely down in the 2D fractal jungle underlying ordinary 4D space, the hole would have to be so small that I just can't imagine how it could exist, given quantum mechanical indefiniteness.

But this paper seems nevertheless relevant because even an astrophysical black hole---the kind we know exist---has to have a PIT. an this paper of Lauscher Reuter gives us one way to imagine that pit.
a fractal foam or jungle----ever more crumpled and curved the closer and more microscopically one looks at it.

I should also remember that as the length scale associated with the pit shrinks, the RECIPROCAL SCALE k (the proximity or energy scale) goes to infinity. In this qeg model that means G(k) and Lambda(k) run.

I think QEG does give us some tools to get a handle on what happens inside black holes, but i personally can't unriddle it. maybe someone else will comment. long day---my bedtime :zzz: