# Scalar field as a null dust

## TL;DR

This paper demonstrates that a massless, minimally coupled scalar field with a null gradient behaves exactly like a null dust fluid, whereas nonminimally coupled scalar fields generally do not, unless they possess a Killing vector symmetry.

## Contribution

It establishes the equivalence of a minimally coupled scalar field to null dust and clarifies conditions under which scalar-tensor gravity scalars can be similarly represented.

## Key findings

- Minimally coupled scalar fields with null gradients are equivalent to null dust.
- Nonminimally coupled scalar fields generally cannot be represented as null dust.
- Scalar-tensor gravity scalars require a Killing vector for null dust representation.

## 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.