Spherically symmetric dissipative anisotropic fluids: A general study

TL;DR

This paper provides a comprehensive analysis of the evolution of spherically symmetric dissipative anisotropic fluids in general relativity, highlighting the relationships between key physical quantities and proposing a condition for energy density homogeneity.

Contribution

It offers a general set of equations for such systems and establishes a necessary and sufficient condition for energy density uniformity, contributing to the understanding of gravitational arrow of time.

Findings

Derived the full evolution equations for dissipative anisotropic fluids

Established the condition for vanishing spatial energy density gradients

Presented solutions illustrating the theoretical framework

Abstract

The full set of equations governing the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses is deployed and used to carry out a general study on the behaviour of such systems, in the context of general relativity. Emphasis is given to the link between the Weyl tensor, the shear tensor, the anisotropy of the pressure and the density inhomogeneity. In particular we provide the general, necessary and sufficient, condition for the vanishing of the spatial gradients of energy density, which in turn suggests a possible definition of a gravitational arrow of time. Some solutions are also exhibited to illustrate the discussion.