Numerical evolution of axisymmetric, isolated systems in General Relativity

TL;DR

This paper introduces a new numerical code for simulating axisymmetric isolated systems in general relativity by solving Friedrich's conformal field equations on a finite grid, enabling comprehensive space-time evolution.

Contribution

The paper presents a novel numerical implementation of Friedrich's conformal field equations for axisymmetric systems, allowing for accurate evolution of asymptotically flat space-times.

Findings

Successful numerical evolution of axisymmetric systems

Effective handling of boundary conditions and axisymmetry

Potential for detailed analysis of gravitational radiation

Abstract

We describe in this article a new code for evolving axisymmetric isolated systems in general relativity. Such systems are described by asymptotically flat space-times which have the property that they admit a conformal extension. We are working directly in the extended `conformal' manifold and solve numerically Friedrich's conformal field equations, which state that Einstein's equations hold in the physical space-time. Because of the compactness of the conformal space-time the entire space-time can be calculated on a finite numerical grid. We describe in detail the numerical scheme, especially the treatment of the axisymmetry and the boundary.