Einstein Equations for a Noncommutative Spacetime of Lie-Algebraic Type
Mathematical Physics
2019-09-06 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Abstract
A general formula is calculated for the connection of a central metric w.r.t.\ a noncommutative spacetime of Lie-algebraic type. This is done by using the framework of linear connections on central bi-modules. The general formula is further on used to calculate the corresponding Riemann tensor and prove the corresponding Bianchi identities and certain symmetries that are essential to obtain a symmetric and divergenceless Einstein Tensor. In particular, the obtained Einstein Tensor is not equivalent to the sum of the noncommutative Riemann tensor and scalar, as in the commutative case, but in addition a traceless term appears.
Cite
@article{arxiv.1705.03499,
title = {Einstein Equations for a Noncommutative Spacetime of Lie-Algebraic Type},
author = {Albert Much and Marcos Rosenbaum and José David Vergara and Diego Vidal-Cruzprieto},
journal= {arXiv preprint arXiv:1705.03499},
year = {2019}
}
Comments
General Revision