On free evolution of self gravitating, spherically symmetric waves

TL;DR

This paper presents a numerical study of the free evolution of a self-gravitating, spherically symmetric scalar field using a simple, symmetric hyperbolic formulation in Eddington-Finkelstein coordinates, demonstrating stable constraint preservation.

Contribution

The authors develop a straightforward, symmetric hyperbolic formulation for evolving self-gravitating scalar fields and analyze gauge instabilities within this framework.

Findings

Successfully reproduce known results of scalar field evolution

Demonstrate stable constraint preservation during numerical evolution

Identify and address gauge instabilities in Eddington-Finkelstein coordinates

Abstract

We perform a numerical free evolution of a selfgravitating, spherically symmetric scalar field satisfying the wave equation. The evolution equations can be written in a very simple form and are symmetric hyperbolic in Eddington-Finkelstein coordinates. The simplicity of the system allow to display and deal with the typical gauge instability present in these coordinates. The numerical evolution is performed with a standard method of lines fourth order in space and time. The time algorithm is Runge-Kutta while the space discrete derivative is symmetric (non-dissipative). The constraints are preserved under evolution (within numerical errors) and we are able to reproduce several known results.