Newtonian gravity on quantum spacetime

TL;DR

This paper demonstrates how introducing gravity into a quantum spacetime model via gauging a specific coefficient leads to modifications in gravitational interactions, potentially informing dark energy research and quantum systems.

Contribution

It shows that gauging a coefficient in the -Minkowski quantum spacetime model introduces gravity and alters effective mass properties.

Findings

Introduction of a constant term in the potential energy.

Weakening and separation of gravitational and inertial masses.

Potential relevance to dark energy and macroscopic quantum systems.

Abstract

The bicrossproduct model \lambda-Minkowski (or `\kappa-Minkowski') quantum spacetime has an anomaly for the action of the Poincar\'e quantum group which was resolved by an extra cotangent direction \theta' not visible classically. We show that gauging a coefficient of \theta' introduces gravity into the model. We solve and analyse the model nonrelativisticaly in a 1/r potential, finding an induced constant term in the effective potential energy and a weakening and separation of the effective gravitational and inertial masses as the test particle Klein-Gordon mass increases. The present work is intended as a proof of concept but the approach could be relevant to an understanding of dark energy and possibly to macroscopic quantum systems.