Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry and General Relativity in the Groupoid Model with a Finite
  Structure Group   In a series of papers we proposed a model unifying general relativity and
quantum mechanics. The idea was to deduce both general relativity and quantum
mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a
transformation groupoid $\Gamma$ determined by the action of the Lorentz group
on the frame bundle $(E, \pi_M, M)$ over space-time $M$. In the present work,
we construct a simplified version of the gravitational sector of this model in
which the Lorentz group is replaced by a finite group $G$ and the frame bundle
is trivial $E=M\times G$. The model is fully computable. We define the
Einstein-Hilbert action, with the help of which we derive the generalized
vacuum Einstein equations. When the equations are projected to space-time
(giving the "general relativistic limit"), the extra terms that appear due to
our generalization can be interpreted as "matter terms", as in
Kaluza-Klein-type models. To illustrate this effect we further simplify the
metric matrix to a block diagonal form, compute for it the generalized Einstein
equations and find two of their "Friedmann-like" solutions for the special case
when $G =\mathbb{Z}_2$. One of them gives the flat Minkowski space-time (which,
however, is not static), another, a hyperbolic, linearly expanding universe.

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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex