Covariant diagonalization of the perfect fluid stress-energy tensor

TL;DR

This paper presents covariant tetrads that diagonalize the stress-energy tensor of a perfect fluid with vorticity, simplifying analysis in relativistic astrophysics and hydrodynamics.

Contribution

Introduction of new covariant tetrads that diagonalize the stress-energy tensor for vorticous perfect fluids, aiding analysis and observer construction in relativistic problems.

Findings

Simplifies the analysis of vorticous relativistic fluids.

Enables straightforward construction of relevant observers.

Provides insights into the origin of inertia in these systems.

Abstract

We introduce new tetrads that manifestly and covariantly diagonalize the stress-energy tensor for a perfect fluid with vorticity at every spacetime point. This new tetrad can be applied and introduce simplification in the analysis of astrophysical relativistic problems where vorticity is present through the Carter-Lichnerowicz equation. This new tetrad also enables the construction in a simple fashion of Euler and Coordinate observers relevant to the Cauchy evolution of many hydrodynamical relativistic problems in the case with no vorticity and the presence of a symmetry where the tetrads are completely analogous to the case with vorticity. We also discuss the origin of inertia in this special case from the standpoint of our new local tetrads.