Asymptotic Solutions of Radiating Stars

TL;DR

This paper analyzes the long-term evolution of radiating star surfaces using a master differential equation, exploring conditions for static end states with charge and cosmological constant influences.

Contribution

It introduces a novel dynamical systems approach to the evolution of radiating stars, deriving criteria for static asymptotic configurations.

Findings

Derived stationary points considering charge and cosmological constant.

Established criteria for initial conditions leading to static asymptotic states.

Applied a dynamical variables approach inspired by cosmology.

Abstract

We investigate the evolution of the surface of radiating stars by studying the asymptotic behaviour of exact solutions initiated via the stationary boundary condition. This boundary condition leads to a master equation in the form of a second-order nonlinear differential equation that describes the evolution of the scale factor. We examine this master equation by introducing a set of dimensionless dynamical variables, motivated by similar approaches in cosmological settings. We derive the stationary points of the system in the presence of charge and a cosmological constant. Furthermore, we construct criteria for the initial conditions in order that the asymptotic limit approaches a static geometry.