The Problem of Constraints in General Relativity: Solution of the Lichnerowicz Equation

Abstract

This paper is dedicated to Andre Lichnerowicz. The splitting property through conformal methods has been discovered by him, as well as the master equation whose solutions on a manifold give admissible initial data sets for Einstein’s equations. In his fundamental paper of 1944 (‘Journal de Mathematiques pures et appliquees) he uses the master equation, which will now be called the Lichnerowicz equation, to construct the first rigorous general solutions of the n-body problem in general relativity.