Higher-dimensional Kundt waves and gyratons

TL;DR

This paper derives exact higher-dimensional Kundt class solutions to Einstein-Maxwell equations, describing gravitational and electromagnetic fields generated by null matter with arbitrary profiles, including special cases like pure gravitational waves and backgrounds with constant curvature.

Contribution

It provides explicit solutions for higher-dimensional Kundt spacetimes with gyratonic matter and electromagnetic fields, extending known 4D solutions to higher dimensions and complex backgrounds.

Findings

Explicit solutions expressed via Green functions

Gyratons and waves on constant curvature backgrounds

Solutions include pure gravitational waves and CSI spacetimes

Abstract

We present and analyze exact solutions of the Einstein-Maxwell equations in higher dimensions which form a large subclass of the Kundt family of spacetimes. We assume that the cosmological constant may be nonvanishing, and the matter consists of a background aligned electromagnetic field and an additional pure radiation (gyratonic) field with a spin. We show that the field equations reduce to a set of linear equations on the transverse space which can be solved exactly and expressed in terms of the Green functions. We thus find explicit exact gyratonic gravitational and electromagnetic fields created by a radiation beam of null matter with arbitrary profiles of energy density and angular momenta. In the absence of the gyratonic matter we obtain pure nonexpanding higher-dimensional gravitational waves. In particular, we investigate gyratons and waves propagating on backgrounds which are a direct-product of 2-spaces of constant curvature. Such type D or 0 background spacetimes generalize 4-dimensional Nariai, anti-Nariai and Plebanski-Hacyan universes, and conformally flat Bertotti-Robinson and Minkowski spaces. These spacetimes belong to a wider class of spaces which admit the Kahler structure related to the background magnetic field. The obtained wave and gyraton solutions are also members of the recently discussed class of spacetimes with constant scalar invariants (CSI) of the curvature tensor.