Killing vectors and anisotropy

TL;DR

This paper explores how an action principle can produce anisotropic fluids with unequal stresses in spacetimes with a spacelike Killing vector, applying the resulting equations to cosmology and cosmic strings.

Contribution

It introduces an action-based framework for modeling anisotropic stresses in spacetimes with a spacelike Killing vector, linking parameters directly to stress anisotropies.

Findings

Derived field equations for anisotropic fluids with spacelike Killing vectors.

Applied equations to anisotropic cosmological expansion.

Extended analysis to Gott-Hiscock cosmic string model.

Abstract

We consider an action that can generate fluids with three unequal stresses for metrics with a spacelike Killing vector. The parameters in the action are directly related to the stress anisotropies. The field equations following from the action are applied to an anisotropic cosmological expansion and an extension of the Gott-Hiscock cosmic string.