Stability Conditions For a Noncommutative Scalar Field Coupled to Gravity

TL;DR

This paper investigates the stability of a noncommutative scalar field in curved spacetime, demonstrating that noncommutativity does not alter stability conditions regardless of the presence of horizons.

Contribution

It shows that stability conditions for a noncommutative scalar field remain unchanged in curved spacetime, extending previous results to noncommutative polynomial potentials.

Findings

Stability conditions are unaffected by noncommutativity.

Results hold in spacetimes with or without horizons.

Noncommutative polynomial potentials maintain stability criteria.

Abstract

We consider a noncommutative scalar field with a covariantly constant noncommutative parameter in a curved space-time background. For a potential as a noncommutative polynomial it is shown that the stability conditions are unaffected by the noncommutativity, a result that is valid irrespective whether space-time has horizons or not.