Relativistic gravitational collapse in comoving coordinates: The post-quasistatic approximation

TL;DR

This paper presents a new iterative method for modeling relativistic gravitational collapse in comoving coordinates, redefining key concepts and demonstrating its application through models inspired by the Schwarzschild interior solution, including adiabatic and non-adiabatic cases.

Contribution

It introduces a novel formulation of the post-quasistatic approximation in comoving coordinates and develops an algorithm for relativistic collapse modeling.

Findings

The method successfully models relativistic collapse scenarios.

Both adiabatic and non-adiabatic cases are effectively handled.

The approach is demonstrated with models based on the Schwarzschild interior solution.

Abstract

A general iterative method proposed some years ago for the description of relativistic collapse, is presented here in comoving coordinates. For doing that we redefine the basic concepts required for the implementation of the method for comoving coordinates. In particular the definition of the post-quasistatic approximation in comoving coordinates is given. We write the field equations, the boundary conditions and a set of ordinary differential equations (the surface equations) which play a fundamental role in the algorithm. As an illustration of the method, we show how to build up a model inspired in the well known Schwarzschild interior solution. Both, the adiabatic and non adiabatic, cases are considered.