Supported by the European Commission, Sixth Framework Programme - Marie Curie Conferences and Training Courses - MSCF-CT-2004-516558 and the Institute of Physics - Classical and Quantum Gravity
The most widely used approach for analyzing solutions of Einstein's gravitational field equations is the initial value formulation, and the key to the initial value formulation is the set of Einstein constraint equations. The study of the constraint equations and their solutions plays a major role in the search to understand the degrees of freedom of the gravitational field, in the search for a theory of gravity consistent with the quantum principle, and in the search for physically realistic models of astrophysical and cosmological gravitational systems. During the past few years, there has been significant progress in our understanding of the Einstein constraints. New ideas from geometric analysis, new techniques from numerical relativity, and new insights from seat-of-the pants physics have all led to this rapid progress.
Some of the topics to be discussed at the Conference are the following:
- initial data engineering via gluing;
- the quasi-spherical method for generating solutions;
- new forms of the conformal decomposition;
- practical attempts to build solutions of the constraint equations which model black hole collisions;
- solutions of the constraints with prescribed boundary behavior;
- rough solutions of the constraints;
- solutions of the constraints with prescribed multipole behavior;
- approximate solutions of the constraints with simplified dynamics ansatze;
- stability of the constraints.