THE CONTINUING EFFECTIVENESS OF THE CONFORMAL METHOD OF SOLVING THE
EINSTEIN CONSTRAINT EQUATIONS
by David Maxwell (University of Alaska)
Abstract:
The Einstein constraint equations are partial differential equations
that arise as a compatibility condition on initial data for the Cauchy
problem of general relativity. The conformal method is a technique,
initiated by Lichnerowicz in 1944 extended by Choquet-Bruhat and York
in the 1970's, for generating solutions of the constraint equations .
It has proved in theory and practice to be the premiere method of
constructing solutions. In this talk I will discuss several recent
advances made by myself and others in constructing black hole
solutions, rough solutions, and glued solutions. All these results
extend the conformal method to new settings. I will also discuss, if
time permits, some long standing open questions concerning the
conformal method.
This talk is intended for a general mathematics audience and much of it
will be devoted to reviewing background material from general
relativity and geometric analysis.