Einstein Equations for a Noncommutative Spacetime of Lie-Algebraic Type

Abstract

A general formula for the curvature of a central metric, w.r.t a noncommutative spacetime of general Lie-algebraic type is calculated by using the generalized braiding formalism. Furthermore, we calculate geometric quantities such as the Riemann tensor and the Ricci tensor and scalar in order to produce quantum corrections to the Einstein field equations. Contents 4 Conclusions and Outlook 13

Gauge theory models on $κ$-Minkowski space: Results and prospects

“…Following this path and inspired by the work of [122], which was revised in [123], [124] defined a version of pseudo-Riemannian calculi of modules over noncommutative algebras. Some authors [125,126,127] tried to constraint gravity on noncommutative spaces by considering general Lie algebraic relations for the space-time noncommutativity.…”

A New Algorithm for the Inverse of Matrices with Noncommuting Entries

“…In particular w.r.t. quantum mechanics and certain trials of quantum gravity, such as noncommutative geometry (see for example [DFR95], [Wes03], [HR06], [BM14] to mention a few examples) we deal with noncommuting elements and from a deformation quantization (see [Wal07] and references therein) point of view (one approach in noncommutative geometry) an effective approach is guided by the following principle: Formulate noncommutative frameworks in terms of commutative theories and add to them corrections that enter in terms of commutators, since commutators contain a deformation parameter (see [BM14,Ces17,MRVVC17] for most recent examples). For calculations of inverses of certain noncommutative generalizations of commutative geometrical Riemannian entities (for example the metric) the use of the quasi-determinant à la [GGRW05] is not very helpful in taking care of orders in the deformation parameter.…”