Minimally coupled scalar fields as imperfect fluids

TL;DR

This paper explores the fluid interpretation of minimally coupled scalar fields in various static and null gradient scenarios, revealing their equivalence to different imperfect fluid types and null dust, with implications for black hole perturbations.

Contribution

It provides a detailed classification of scalar fields as imperfect fluids or null dust based on their gradient properties and proposes a variational principle for these descriptions.

Findings

Scalar fields with spatial gradients can be modeled as imperfect fluids or null dust.

Null gradient scalar fields are equivalent to imperfect fluids of type II.

A suitable action in terms of fluid pressure components is proposed for each case.

Abstract

We revisit the issue of the fluid description of minimally coupled scalar fields. While in a cosmological setup the interpretation of a time-evolving scalar field as a perfect fluid is well-understood, the situation is more intricate when the scalar field is static, but has a spatial gradient, a situation motivated by black hole perturbations in scalar-tensor theories. Then the scalar field is interpreted as either a particular imperfect fluid of type I or a superposition of a pair of leftgoing (incoming) and rightgoing (outgoing) null dusts with a perfect fluid. Finally, when the scalar gradient is null, it is equivalent to an imperfect fluid of type II, degenerating into null dust when the energy conditions are imposed. We also propose the suitable action in terms of the fluid pressure components for each case and discuss the variational principle for a generic class of minimally coupled scalar fields.