Cylindrically Symmetric Relativistic Fluids: A Study Based on Structure Scalars

TL;DR

This paper develops a scalar-based formalism for analyzing the structure and evolution of cylindrically symmetric, dissipative relativistic fluids, revealing their fundamental properties and providing explicit solutions in static cases.

Contribution

It introduces a set of structure scalars derived from the Riemann tensor for cylindrically symmetric fluids, extending previous spherical symmetry results to this geometry.

Findings

Structure scalars relate to energy density and anisotropy.

Explicit solutions are obtained for static configurations.

Scalars influence the dynamics of dissipative fluids.

Abstract

The full set of equations governing the structure and the evolution of self--gravitating cylindrically symmetric dissipative fluids with anisotropic stresses, is written down in terms of scalar quantities obtained from the orthogonal splitting of the Riemann tensor (structure scalars), in the context of general relativity. These scalars which have been shown previously (in the spherically symmetric case) to be related to fundamental properties of the fluid distribution, such as: energy density, energy density inhomogeneity, local anisotropy of pressure, dissipative flux, active gravitational mass etc, are shown here to play also a very important role in the dynamics of cylindrically symmetric fluids. It is also shown that in the static case, all possible solutions to Einstein equations may be expressed explicitly through three of these scalars.