3+1 formalism and bases of numerical relativity - LUTh ...

Preface
These notes are the written version of lectures given in the fall of 2006 at the General Relativity
Trimester at the Institut Henri Poincaré in Paris [1] and (for Chap. 8) at the VII Mexican School
on Gravitation and Mathematical Physics in Playa del Carmen (Mexico) [2].
The prerequisites are those of a general relativity course, at the undergraduate or graduate
level, like the textbooks by Hartle [155] or Carroll [79], of part I of Wald’s book [265], as well
as track 1 of Misner, Thorne and Wheeler book [189].
The fact that this is lecture notes and not a review article implies two things:
• the calculations are rather detailed (the experienced reader might say too detailed), with
an attempt to made them self-consistent and complete, trying to use as less as possible
the famous sentences “as shown in paper XXX” or “see paper XXX for details”;
• the bibliographical references do not constitute an extensive survey of the mathematical
or numerical relativity literature: articles have been cited in so far as they have a direct
connection with the main text.
I thank Thibault Damour and Nathalie Deruelle — the organizers of the IHP Trimester, as
well as Miguel Alcubierre, Hugo Garcia-Compean and Luis Urena — the organizers of the VII
Mexican school, for their invitation to give these lectures. I also warmly thank Marcelo Salgado
for the perfect organization of my stay in Mexico. I am indebted to Nicolas Vasset for his careful
reading of the manuscript. Finally, I acknowledge the hospitality of the Centre Émile Borel of
the Institut Henri Poincaré, where a part of these notes has been written.
Corrections and suggestions for improvement are welcome at eric.gourgoulhon@obspm.fr.