Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. II. The evolution equations

TL;DR

This paper presents numerical methods for solving Einstein's conformal field equations, focusing on gauge choices, boundary treatment, and radiation extraction in the hyperboloidal initial value problem.

Contribution

It introduces specific numerical techniques for evolution equations derived from Friedrich's conformal field equations, enhancing stability and radiation analysis.

Findings

Effective boundary treatment methods developed

Gauge source functions optimized for stability

Radiation extraction process demonstrated

Abstract

This is the second in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper the numerical methods used to solve the system of evolution equations obtained from the conformal field equations. In particular we discuss in detail the choice of gauge source functions and the treatment of the boundaries. Of particular importance is the process of ``radiation extraction'' which can be performed in a straightforward way in the present formalism.