An evolution of adiabatic matter: A case for the quasistatic regime

TL;DR

This paper explores the evolution of adiabatic matter in the quasistatic regime, establishing a connection between ADM 3+1 formalism and flux-conservative fluid equations, revealing slow, non-shear-free matter dynamics.

Contribution

It introduces a post-quasi-static approximation in radiation coordinates for adiabatic perfect fluids, linking ADM formalism with flux-conservative equations in spherical symmetry.

Findings

Derived flux-conservative fluid equations in spherical symmetry.

Established adiabatic matter evolution in the quasistatic regime.

Showed matter is slow-moving, non-shear-free, and non-geodesic.

Abstract

We establish the connection between the standard ADM 3+1 treatment of matter with its characteristic equivalent, in the context of spherical symmetry. The flux-conservative rendition of the fluid equations are obtained. Considering adiabatic distributions of perfect fluid, we evolve the system using the so-called post-quasi-static approximation in radiation coordinates. We obtain an adiabatic matter evolution in the quasi-static regime or slow motion, which is not shear-free nor geodesic.