Scalar field as a null dust

Abstract: We show that a canonical, minimally coupled scalar field which is non-self interacting and massless is equivalent to a null dust fluid (whether it is a test or a gravitating field), in a spacetime region in which its gradient is null. Under similar conditions, the gravitating and nonminimally coupled Brans-Dicke-like scalar of scalar-tensor gravity, instead, cannot be represented as a null dust unless its gradient is also a Killing vector field.