Exploring AdS Waves Via Nonminimal Coupling

TL;DR

This paper investigates nonminimally coupled scalar fields in three-dimensional AdS spacetimes, revealing a unique self-interaction potential and exploring the properties of gravitational waves, including mass effects and conformal relations.

Contribution

It introduces a specific self-interaction potential for nonminimally coupled scalars in AdS waves and analyzes their properties, including mass effects and relations to pp waves.

Findings

Existence of a unique self-interaction potential depending on a coupling constant.

Identification of conditions for massless and tachyonic scalar fields.

Establishment of a conformal relation between AdS and pp wave sources.

Abstract

We consider nonminimally coupled scalar fields to explore the Siklos spacetimes in three dimensions. Their interpretation as exact gravitational waves propagating on AdS restrict the source to behave as a pure radiation field. We show that the related pure radiation constraints single out a unique self-interaction potential depending on one coupling constant. For a vanishing coupling constant, this potential reduces to a mass term with a mass fixed in terms of the nonminimal coupling parameter. This mass dependence allows the existence of several free cases including massless and tachyonic sources. There even exists a particular value of the nonminimal coupling parameter for which the corresponding mass exactly compensates the contribution generated by the negative scalar curvature, producing a genuinely massless field in this curved background. The self-interacting case is studied in detail for the conformal coupling. The resulting gravitational wave is formed by the superposition of the free and the self-interaction contributions, except for a critical value of the coupling constant where a non-perturbative effect relating the strong and weak regimes of the source appears. We establish a correspondence between the scalar source supporting an AdS wave and a pp wave by showing that their respective pure radiation constraints are conformally related, while their involved backgrounds are not. Finally, we consider the AdS waves for topologically massive gravity and its limit to conformal gravity.