Stability Conditions For a Noncommutative Scalar Field Coupled to Gravity via the Positive Energy Theorem

TL;DR

This paper investigates the stability of a noncommutative scalar field coupled to gravity using the positive energy theorem, finding that stability conditions resemble those in the commutative case, regardless of horizons.

Contribution

It demonstrates that stability conditions for noncommutative scalar fields with polynomial potentials are similar to commutative cases, even in spacetimes with horizons.

Findings

Stability conditions are similar to commutative scalar fields.

Results hold for spacetimes with horizons.

Positive energy theorem applies to noncommutative fields.

Abstract

The stability requirements for a noncommutative scalar field coupled to gravity is investigated through the positive energy theorem. It is shown that for a noncommutative scalar with a polynomial potential, the stability conditions are similar to the ones for the commutative case. This result remains valid even whether the space-time has horizons.