Newtonian gravity on quantum spacetime
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.
Cite
@article{arxiv.1109.6190,
title = {Newtonian gravity on quantum spacetime},
author = {Shahn Majid},
journal= {arXiv preprint arXiv:1109.6190},
year = {2012}
}
Comments
11 pages 1 figure