Newtonian gravity on quantum spacetime
School of Mathematical Sciences Queen Mary University of London 327 Mlle End Rd London E1 4NS
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Published online: 10 April 2014
The bicrossproduct model λ-Minkowski (or ‘κ-Minkowski’) quantum space-time has an anomaly for the action of the Poincaré quantum group which was resolved by an extra cotangent direction θ’ not visible classically. We show that gauging a coefficient of θ′ 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.
© Owned by the authors, published by EDP Sciences, 2014
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