Higher-dimensional AdS waves and pp-waves with conformally related sources

TL;DR

This paper demonstrates that higher-dimensional AdS and pp-waves supported by scalar fields with nonminimal coupling are conformally related, with constraints fixing scalar dependence and self-interactions, revealing a deep connection between these gravitational waves.

Contribution

It shows that pure radiation constraints for AdS and pp-waves with scalar fields are conformally related, establishing a novel link between these solutions in higher dimensions.

Findings

Pure radiation constraints fix scalar field dependence.

The two sets of constraints are conformally related.

The potential for AdS waves derives from pp-wave self-interactions.

Abstract

AdS waves and pp-waves can only be supported by pure radiation fields, for which the only nonvanishing component of the energy-momentum tensor is the energy density along the retarded time. We show that the nonminimal coupling of self-gravitating scalar fields to the higher-dimensional versions of these exact gravitational waves can be done consistently. In both cases, the resulting pure radiation constraints completely fix the scalar field dependence and the form of the allowed self-interactions. More significantly, we establish that the two sets of pure radiation constraints are conformally related for any nonminimal coupling, in spite of the fact that the involved gravitational fields are not necessarily related. In this correspondence, the potential supporting the AdS waves emerges from the self-interaction associated to the pp-waves and a self-dual condition naturally satisfied by the pp-wave scalar fields.