Axially symmetric dissipative fluids in the quasi--static approximation

TL;DR

This paper investigates axially symmetric dissipative fluids under the quasi-static approximation using the 1+3 formalism, deriving invariant velocities and analyzing their physical implications, including conditions for gravitational radiation.

Contribution

It introduces invariant velocities to define the quasi-static regime and explores the physical consequences of dissipation, vorticity, and shear in such fluids.

Findings

Velocities can change sign within the fluid, affecting physical interpretation.

States of gravitational radiation can exist in quasi-static regimes but are physically irrelevant due to infinite duration.

The formalism clarifies conditions under which dissipative effects influence fluid dynamics.

Abstract

Using a framework based on the $1+3$ formalism we carry out a study on axially and reflection symmetric dissipative fluids, in the quasi--static regime. We first derive a set of invariantly defined "velocities", which allow for an inambiguous definition of the quasi--static approximation. Next we rewrite all the relevant equations in this aproximation and extract all the possible, physically relevant, consequences ensuing the adoption of such an approximation. In particular we show how the vorticity, the shear and the dissipative flux, may lead to situations where different kind of "velocities" change of sign within the fluid distribution with respect to theirs sign on the boundary surface. It is shown that states of gravitational radiation are not {\it a priori} incompatible with the quasistatic--regime. However, any such state must last for an infinite period of time, thereby diminishing its physical relevance.