Non conducting spherically symmetric fluids

TL;DR

This paper investigates spherically symmetric spacetimes with zero flux, providing a geometric and physical analysis that explains properties like shearfree conditions in perfect fluids with homogeneous energy density.

Contribution

It offers a novel geometric and Einstein equation-based framework for analyzing zero flux spherically symmetric fluids, clarifying conditions like shearfree behavior.

Findings

Shearfree condition for perfect fluids with homogeneous energy density.

Geometric characterization of zero flux spherically symmetric spacetimes.

Formal inversion method for Einstein's equations in this context.

Abstract

A class of spherically symmetric spacetimes invariantly defined by a zero flux condition is examined first from a purely geometrical point of view and then physically by way of Einstein's equations for a general fluid decomposition of the energy-momentum tensor. The approach, which allows a formal inversion of Einstein's equations, explains, for example, why spherically symmetric perfect fluids with spatially homogeneous energy density must be shearfree.