Exact pp-wave solutions in shift-symmetric higher-order scalar-tensor theories

TL;DR

This paper finds exact gravitational wave solutions in shift-symmetric higher-order scalar-tensor theories, revealing conditions for stealth scalar fields and analyzing their behavior under disformal transformations.

Contribution

It demonstrates the existence of exact pp-wave solutions with stealth scalar fields in shift-symmetric higher-order scalar-tensor theories, extending the understanding of nonlinear radiative spacetimes.

Findings

Stealth pp-wave solutions coexist with nontrivial scalar fields without backreaction.

Under certain conditions, the field equations reduce to a Laplace equation similar to GR.

Disformal transformations preserve the Brinkmann form but generally destroy the stealth property.

Abstract

We investigate exact plane-fronted gravitational wave (pp-wave) solutions within the framework of shift-symmetric quadratic-order higher-order scalar--tensor (HOST) theories. These solutions represent fully nonlinear radiative spacetimes that extend beyond the linearized approximation. We demonstrate that under the algebraic conditions on the coupling functions, the gravitational field equations reduce to a two-dimensional Laplace equation for the wave profile, recovering the structural form of vacuum general relativity (GR). By adopting a scalar field ansatz that depends linearly on transverse coordinates and arbitrarily on the retarded null coordinate, we maintain a constant kinetic term of the scalar field. This configuration allows for a \emph{stealth pp-wave} solution, where a nontrivial scalar field profile coexists with the gravitational wave without backreacting on the spacetime geometry. We further show that these stealth configurations are fully compatible with the degeneracy conditions of Class-Ia DHOST theories and satisfy current observational constraints. Finally, we examine the behavior of these solutions under disformal transformations, revealing that while the Brinkmann form is preserved, the stealth property is generically lost due to the mixing of scalar and tensor degrees of freedom. These results establish the robustness of pp-wave solutions in viable DHOST frameworks and highlight their utility for probing nonlinear effects in modified gravity.