Mathematical Relativity: New Ideas and Developments

Simonetta Frittelli, Duquesne University, simo@mayu.physics.duq.edu
This meeting took place in Bad Honnef, on the shores of the Rhine, Germany, on March 1-5, 2004. This was the latest in an ongoing series of seminars sponsored by the Heraeus foundation, the most important German private funding institution in physics and one that cooperates frequently with the German Physical Society.

The meeting was principally aimed at a broad audience that included a large representation of junior participants. There were 60-minute plenary talks in the morning, and 30-minute selected contributed talks in the afternoon. The plenary talks covered mostly recent developments in topological, analytical and numerical methods in mathematical relativity. Undoubtedly by thoughtful design on the part of the organizers (Jörg Frauendiener, Domenico Giulini and Volker Perlick), many plenary talks complemented or supplemented each other in a refreshingly cohesive way.

The conference was opened by Bobby Beig (Vienna) with a description of hyperbolic equations for matter fields. This was followed by a presentation on the space of null geodesics by Robert Low (UK), and a discussion about the geometry of pp-wave spacetimes (which generalize classical plane waves) by Miguel Sanchez (Spain).

In what was characterized as ``the revenge of the physicists'' by some participants, the presentations of the second day all revolved around the interplay between numerical and analytical issues, with talks delivered by Jeff Winicour, myself, Luis Lehner and Beverly Berger (all USA). These talks were meant to illustrate not only how analysis and geometry can guide numerical efforts, but, conversely, how numerical simulations can provide clues for analytic developments.

Bob Wald (USA) opened the third day with a review of conserved quantities associated with hypersurfaces that go to null infinity in asymptotically flat spacetimes, which prompted a curious dialogue between Bob and Roger Penrose (UK) about what ``normal'' people refer to as the ``problem'' of angular momentum. This was followed by the revenge of the mathematicians Paul Ehrlich (USA), with an anecdotic perspective on the influence of the book Global Lorentzian Geometry, and Antonio Masiello (Italy), who spoke about the Avez-Seifert theorem for the relativistic Lorentz equation. The day ended with an evening talk by Roger Penrose about the three F's in modern physical theories: Fashion (strings), Faith (quantum mechanics) and Fantasy (inflation).

Undaunted by the implications of Penrose's address, Alan Rendall (Germany) delivered an impression of good old inflation from a mathematician's point of view the very next day, followed by Helmut Friedrich (Germany) on conformal infinity and its connection to the Newman-Penrose constants, and Sergio Dain (Germany) with a description of the use of trapped surfaces as boundaries for the constraint equations on initial values for black hole spacetimes.

The meeting closed with talks by Greg Galloway (USA) on asymptotically deSitter spacetimes, and Laszlo Szabados (Hungary) on the definition of center of mass associated with Cauchy surfaces in asymptotically flat spacetimes.

The venue for the meeting was highly conducent to interaction between junior and senior participants. This was a large mansion (the Physikzentrum) featuring accomodations, dining and a state-of-the-art conference room. There was a common room where breakfast and lunch were served at tables for six people, and an old-fashioned basement cellar where a buffet dinner was available and where much informal social interaction took place in the evenings (apparently including fortune readings). A conference picture can be accessed at http://mayu.physics.duq.edu/~simo/badhonnef04.html

The substance of the the plenary talks will be published as a Springer volume in the near future. The complete program including the abstracts of the contributed talks and posters is available online at http://www.tat.physik.uni-tuebingen.de/~heraeus/.


Jorge Pullin 2004-03-12