Central tetrads and quantum spacetimes

Abstract

In this paper, we perform a parallel analysis to the model proposed in [E. J. Beggs and S. Majid, Gravity induced from quantum spacetime, Class. Quantum Grav. 31 (2014) 035020, arXiv: 1305.2403 [gr-qc]]. By considering the central co-tetrad (instead of the central metric), we investigate the modifications in the gravitational metrics coming from the noncommutative spacetime of the [Formula: see text]-Minkowski type in four dimensions. The differential calculus corresponding to a class of Jordanian [Formula: see text]-deformations provides metrics, which lead either to cosmological constant or spatial curvature type solutions of nonvacuum Einstein equations. Among vacuum solutions, we find pp-wave type.