Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic Quantization of General Relativity \`a la Ricci-Flow   We follow a new pathway to the definition of the Stochastic Quantization
(SQ), first proposed by Parisi and Wu, of the action functional yielding the
Einstein equations. Hinging on the functional similarities between the
Ricci-Flow equation and the SQ Langevin equations, we push forward a novel
approach in which the stochastic time converges to the proper time of a
space-like foliation in the equilibrium limit. This procedure in turn requires
adding to the usual symmetric connection a projective Weyl term that does not
modify the classical equations of motion. Furthermore, we express the starting
system of equations using the Arnowitt-Deser-Misner (ADM) variables and their
conjugated Hamiltonian momenta. Such a choice is instrumental for understanding
the newly derived equations in terms of the breaking the diffeomorphism
invariance of the classical theory, which will hold on average at the steady
state. We comment on the physical interpretation of the Ricci flow equations,
and argue how they can naturally provide, in a geometrical way, the
renormalization group equation for gravity theories. In the general setting,
the equation associated to the shift vector yields the Navier-Stokes equation
with a stochastic source. Moreover, we show that the fluctuations of the metric
tensor components around the equilibrium configurations, far away from the
horizon of a Schwarzschild black hole, are forced by the Ricci flow to follow
the Kardar-Parisi-Zhang equation, whose probabilistic distribution can yield an
intermittent statistics. We finally comment on the possible applications of
this novel scenario to the cosmological constant, arguing that the Ricci flow
may provide a solution to the Hubble tension, as a macroscopic effect of the
quantum fluctuation of the metric tensor.

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The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math