Introduction

5.1 Introduction

In this section, we restrict ourselves to problems in which time does not appear explicitly. This is especially the case for systems, that are stationary, like neutron stars in rotation or binary systems in circular orbits. The computation of initial data also falls into this class, given that it consists in finding a particular solution of Einstein’s equations at a given time only. Indeed, when using the standard 3+1 decomposition of spacetime, the initial data that are passed to the evolution equations cannot be totally arbitrary and must satisfy a set of equations called Einstein’s constraint equations. For more details of the initial data problem we refer to the review by Cook [61

]. So, in treating the problems considered here, one may forget about the issues specific to time presented in Section 4.

It must be said that spectral methods are not the only technique that has been successfully used to generate stationary spacetimes. [24 , 222 , 60 , 147 ] give some examples of this, especially in the case of binary systems, for neutron stars or black holes. More references can be found in [61 ].