Noncommutative Einstein-Maxwell pp-waves

TL;DR

This paper explores solutions to noncommutative Einstein-Maxwell equations, revealing how noncommutativity modifies pp-wave spacetimes and electromagnetic waves, with corrections appearing at first order in the noncommutativity parameters.

Contribution

It provides the first explicit solutions describing noncommutative Einstein-Maxwell pp-waves, including metric and electromagnetic field corrections at first order in noncommutativity.

Findings

Noncommutative corrections modify the spacetime metric via a conformal factor.

Electromagnetic waves exhibit constant polarization, higher harmonics, and inhomogeneous susceptibility.

Noncommutativity affects the separation between points in null surfaces.

Abstract

The field equations coupling a Seiberg-Witten electromagnetic field to noncommutative gravity, as described by a formal power series in the noncommutativity parameters $\theta^{\alpha\beta}$, is investigated. A large family of solutions, up to order one in $\theta^{\alpha\beta}$, describing Einstein-Maxwell null pp-waves is obtained. The order-one contributions can be viewed as providing noncommutative corrections to pp-waves. In our solutions, noncommutativity enters the spacetime metric through a conformal factor and is responsible for dilating/contracting the separation between points in the same null surface. The noncommutative corrections to the electromagnetic waves, while preserving the wave null character, include constant polarization, higher harmonic generation and inhomogeneous susceptibility. As compared to pure noncommutative gravity, the novelty is that nonzero corrections to the metric already occur at order one in $\theta^{\alpha\beta}$.