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 ${\theta }^{\alpha \beta }$.

• Received 27 July 2006

DOI:https://doi.org/10.1103/PhysRevD.74.105004