While I find asymptotic safety an intriguing idea, it would be disturbing for a truly fundamental model of gravity to have singularities.
http://arxiv.org/abs/1008.2768
Asymptotic Safety, Singularities, and Gravitational Collapse
Roberto Casadio, Stephen D.H. Hsu, Behrouz Mirza
Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers the possibility that a predictive theory of quantum gravity can be obtained from the quantization of classical general relativity. However, it is unclear what becomes of the singularities of classical general relativity, which, it is hoped, might be resolved by quantum effects. We study dust collapse with a running gravitational coupling and find that a future singularity can be avoided if the coupling becomes exactly zero at some finite energy scale. The singularity can also be avoided (pushed off to infinite proper time) if the coupling approaches zero sufficiently rapidly at high energies. However, the evolution deduced from perturbation theory still implies a singularity at finite proper time.
An Italian, an Iranian, and an American physicist walk into a bar ...
1 comment:
You people have found a of getting rid of the singularity, but something else you did in the paper doesn't lead to conclude that a perturbative is not possible. Notice that eq. 3.8, unless for constant G, is a non linear equation, whose approximate solutions only works around the vicinity of parameters, yet you try to find a relation that should relate u and p through out the whole space, which you call "self - consistent". You shouldn`t conclude that they do not have a non-perturbative formulation, because 3.9 is an example of one, but that there is not possible to find a unique perturbative expansion for all the space: only local ones are possible.
I think this is a very beautiful solution that you find, but only if you look from this angle.
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