Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On geodesics in space-times with a foliation structure: A spectral
  geometry approach   Motivated by the Horava-Lifshitz type theories, we study the physical motion
of matter coupled to a foliated geometry in non-diffeomorphism invariant way.
We use the concept of a spectral action as a guiding principle in writing down
the matter action. Based on the deformed Dirac operator compatible with the
reduced symmetry - foliation preserving diffeomorphisms, this approach provides
a natural generalization of the minimal coupling. Focusing on the IR version of
the Dirac operator, we derive the physical motion of a test particle and
discuss in what sense it still can be considered as a geodesic motion for some
modified geometry. We show that the apparatus of non-commutative geometry could
be very efficient in the study of matter coupled to the Horava-Lifshitz
gravity.

32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat