On the flow of perfect energy tensors

TL;DR

This paper derives the precise conditions under which a unit timelike vector field can represent the flow of a divergence-free perfect fluid energy tensor, providing a detailed kinematic classification and solutions for energy density and pressure.

Contribution

It offers a complete kinematic characterization of conservative perfect fluid flows, identifying eighteen classes and their associated constraints and solutions.

Findings

Eighteen classes of fluid flows identified based on differential concomitants.

Explicit conditions for the energy density and pressure functions are derived.

Provides a framework for analyzing perfect fluid energy tensors in relativistic contexts.

Abstract

The necessary and sufficient conditions are obtained for a unit time-like vector field $u$ to be the unit velocity of a divergence-free perfect fluid energy tensor. This plainly kinematic description of a conservative perfect fluid requires considering eighteen classes defined by differential concomitants of $u$. For each of these classes, we get the additional constraints that label the flow of a conservative energy tensor, and we obtain the pairs of functions $\{\rho,p\}$, energy density and pressure, which complete a solution to the conservation equations.