Axially symmetric dissipative fluids in the quasi--static approximation

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.

10 pages. arXiv admin note: text overlap with arXiv:1404.1176. Some typos corrected. To appear in Int.J.Mod.Phys.D

References in corpus (7)

• Shearing Expansion-free Spherical Anisotropic Fluid Evolution
• Dynamical laws of superenergy in General Relativity
• Dissipative collapse of axially symmetric, general relativistic, sources: A general framework and some applications
• Shear-free axially symmetric dissipative fluids
• Why does gravitational radiation produce vorticity?
• Separating expansion and collapse in general fluid models with heat flux
• An evolution of adiabatic matter: A case for the quasistatic regime

Cited by in corpus (4)

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• Quasi Static Evolution of Compact Objects in Modified Gravity
• The theory of gravitation: A tale of many questions and few answers