Central tetrads and quantum spacetimes

TL;DR

This paper explores how noncommutative $kappa$-Minkowski spacetime affects gravitational metrics by using central co-tetrads, revealing solutions like cosmological constants, spatial curvature, and pp-waves.

Contribution

It introduces a novel approach using central co-tetrads to analyze noncommutative spacetime effects on gravity, extending previous models.

Findings

Metrics with cosmological constant or spatial curvature solutions.

Existence of pp-wave type vacuum solutions.

Modified gravitational solutions due to noncommutative geometry.

Abstract

In this paper, we perform a parallel analysis to the model proposed in [25]. 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 $\kappa$-Minkowski type in four dimensions. The differential calculus corresponding to a class of Jordanian $\kappa$-deformations provides metrics, which lead either to cosmological constant or spatial curvature type solutions of non-vacuum Einstein equations. Among vacuum solutions, we find pp-wave type.