Fuzzy-pp Waves

TL;DR

This paper develops a noncommutative geometric framework for plane-wave solutions in gravity, modifying classical solutions to include noncommutative algebraic structures and differential calculus.

Contribution

It introduces a noncommutative version of a gravitational plane-wave solution, extending classical solutions with algebraic and differential calculus structures supporting the metric.

Findings

1. Constructed a noncommutative algebra supporting the metric.

2. Demonstrated non-anticommutativity of 1-forms depending on metric deviation.

3. Provided a specific example of a noncommutative plane-wave solution.

Abstract

We present a noncommutative version of a plane-wave solution to the gravitational field equations. We start with a given classical solution, admittedly rather simple, and construct an algebra and a differential calculus which supports the metric. In the particular solution presented as an example the 1-forms do not anticommute, to a degree which depends on the amplitude of the deviation of the metric from the standard Minkowski metric.