Linear stability of noncommutative spectral geometry

TL;DR

This paper demonstrates the linear stability of noncommutative spectral geometry models, including vacuum and nonvacuum cases, by analyzing the spectral action and showing the equations of motion reduce to Einstein's equations and the Hamiltonian is bounded below.

Contribution

It establishes the linear stability of noncommutative spectral geometry models in both vacuum and nonvacuum scenarios through spectral action analysis.

Findings

Equations of motion reduce to Einstein's equations in vacuum.

Hamiltonian is bounded from below in nonvacuum case.

The theory is linearly stable in both scenarios.

Abstract

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.