Abstract

Brill waves are the simplest (non-trivial) solutions to the vacuum constraints of general relativity. They are also rich enough in structure to allow us believe that they capture, at least in part, the generic properties of solutions of the Einstein equations. As such, they deserve the closest attention. This article illustrates this point by showing how Brill waves can be used to investigate the structure of conformal superspace.

INTRODUCTION

From time to time I amuse myself by mentally assembling a list of articles I would like to have written. The candidates for this list have to satisfy a number of criteria. Naturally, they have to be both important and interesting to me. Equally, they have to contain results that I can convince myself, however unreasonably, that I could have obtained. Every time I make my list I am struck again by the number of articles by Dieter Brill appearing on it. At first glance, this is explained by the large overlap between our interests. In reality, however, the explanation is to be found by considering the kind of article that Dieter has written over the years and the way in which he manages to convey major insights in a deceptively simple fashion.