Dieter Brill: A Spacetime Perspective

Summary

This review of Dieter Brill's publications is intended not only as a tribute but as a useful guide to the many insights, results, ideas, and questions with which Dieter has enriched the field of general relativity. We have divided up Dieter Brill's work into several naturally defined categories, ordered in a quasi-chronological fashion. References [n] are to Brill's list of publications near the end of this volume. Inevitably, the review covers only a part of Brill's work, the part defined primarily by the areas with which the authors of the review are most familiar.

GEOMETRODYNAMICS—GETTING STARTED

In a 1977 letter to John Wheeler, his thesis supervisor, Brill recalled that after spin 1/2 failed [1] to fit into Wheeler's geometrodynamics program he asked John “for a ‘sure-fire’ thesis problem, and [John] suggested positivity of mass.” Brill's Princeton Ph.D. thesis [A, 2] provided a major advance in Wheeler's “Geometrodynamics” program. By studying possible initial values, Brill showed that there exist solutions of the empty-space Einstein equations that are asymptotically flat and not at all weak. Moreover, in the large class of examples he treated, all were seen to have positive energy. Although described only at a moment of time symmetry, these solutions were interpreted as pulses of incoming gravitational radiation that would proceed to propagate as outgoing radiation.