Earliest stages of the non-equilibrium in axially symmetric, self-gravitating, dissipative fluids

TL;DR

This study investigates the immediate non-equilibrium behavior of axially symmetric, dissipative fluids after departure from equilibrium, highlighting the critical role of vorticity and initial signs of dynamic evolution in specific fluid variables.

Contribution

It identifies the earliest time scale of non-equilibrium onset in dissipative fluids and links it to the time derivative of vorticity, revealing initial signs of evolution in specific tensor components.

Findings

Non-equilibrium onset depends on a function related to vorticity derivative.

Only certain tensor components show early signs of evolution.

Gravitational radiation emission begins at later times.

Abstract

We report a study on axially and reflection symmetric dissipative fluids, just after its departure from hydrostatic and thermal equilibrium, at the smallest time scale at which the first signs of dynamic evolution appear. Such a time scale is smaller than the thermal relaxation time, the thermal adjustment time and the hydrostatic time. It is obtained that the onset of non--equilibrium will critically depend on a single function directly related to the time derivative of the vorticity. Among all fluid variables (at the time scale under consideration), only the tetrad component of the anisotropic tensor in the subspace orthogonal to the four--velocity and the Killing vector of axial symmetry, shows signs of dynamic evolution. Also, the first step toward a dissipative regime begins with a non--vanishing time derivative of the heat flux component along the meridional direction. The magnetic part of the Weyl tensor vanishes (not so its time derivative), indicating that the emission of gravitational radiation will occur at later times. Finally, the decreasing of the effective inertial mass density, associated to thermal effects, is clearly illustrated.