Scalar Fields Nonminimally Coupled to pp Waves

TL;DR

This paper explores pp wave solutions in three-dimensional gravity with nonminimally coupled scalar fields, analyzing free and self-interacting cases across various gravity theories, including topologically massive and conformal gravity.

Contribution

It introduces new pp wave solutions with nonminimally coupled scalar fields in different gravity models, including conformal gravity, and examines their properties and extensions.

Findings

Self-interacting scalar fields do not behave like waves, depending only on the wave-front coordinate.

New pp wave solutions of conformal gravity are obtained at zero topological mass for arbitrary nonminimal coupling.

Solutions are extended to include self-interacting scalar fields in conformal gravity.

Abstract

Here, we report pp waves configurations of three-dimensional gravity for which a scalar field nonminimally coupled to them acts as a source. In absence of self-interaction the solutions are gravitational plane waves with a profile fixed in terms of the scalar wave. In the self-interacting case, only power-law potentials parameterized by the nonminimal coupling constant are allowed by the field equations. In contrast with the free case the self-interacting scalar field does not behave like a wave since it depends only on the wave-front coordinate. We address the same problem when gravitation is governed by topologically massive gravity and the source is a free scalar field. From the pp waves derived in this case, we obtain at the zero topological mass limit, new pp wave solutions of conformal gravity for any arbitrary value of the nonminimal coupling parameter. Finally, we extend these solutions to the self-interacting case of conformal gravity.