Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear stability of noncommutative spectral geometry   We consider the spectral action within the context of a 4-dimensional
manifold with torsion and show that, in the vacuum case, the equations of
motion reduce to Einstein's equations, securing the linear stability of the
theory. To subsequently investigate the nonvacuum case, we consider the
spectral action of an almost commutative torsion geometry and show that the
Hamiltonian is bounded from below, a result which guarantees the linear
stability of the theory.

7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin