Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. I. The conformal field equations

TL;DR

This paper introduces a numerical approach to solving Friedrich's conformal field equations for Einstein's gravity, emphasizing the potential benefits and detailed derivation in spinor formalism for future research.

Contribution

It provides a detailed derivation of the conformal field equations in spinor formalism and discusses the applicability of the conformal method to numerical relativity.

Findings

The conformal field equations can be effectively formulated in spinor formalism.

Applying the conformal method offers promising advantages for numerical solutions.

The paper establishes a reference framework for future numerical implementations.

Abstract

This is the first 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 why one should be interested in applying the conformal method to physical problems and why there is good hope that this might even be a good idea from the numerical point of view. We describe in detail the derivation of the conformal field equations in the spinor formalism which we use for the implementation of the equations, and present all the equations as a reference for future work. Finally, we discuss the implications of the assumptions of a continuous symmetry.