Exploring AdS waves via nonminimal coupling

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Abstract
We consider nonminimally coupled scalar fields to explore the Siklos spacetimes in three dimensions. Their interpretation as exact gravitational waves propagating on AdS space 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 nonperturbative 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.

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