Statistics – Computation
Scientific paper
Feb 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004cqgra..21.....b&link_type=abstract
Classical and Quantum Gravity, Volume 21, Issue 3, pp. (2004).
Statistics
Computation
1
Scientific paper
It is hard to find an area of mathematical relativity that has not been profoundly influenced and advanced by the work of Vincent Moncrief. He has done groundbreaking work on everything from his studies of gravitational radiation production by astrophysical systems to his model proofs of strong cosmic censorship. His work on the manifold structure of the space of solutions of the Einstein constraint equations, and on methods for systematically constructing such solutions, has done much to define and shape that field of inquiry, while his work on long time existence for the Yang-Mills and Einstein equations has significantly advanced the study of nonlinear hyperbolic PDE theory.
The underlying theme to this very diverse portfolio of work is this: throughout his career, Vince has consistently chosen to attack those problems in general relativity which are both central to understanding the physical content of the gravitational physics of the theory, and are amenable to rigorous mathematical analysis. Combining an uncanny physical insight with a deep mathematical skill, and adding a legendary degree of carefulness, Vince has remade a great many of the areas of mathematical general relativity.
The best known early example of Vince's unique style is the tour de force represented by his analyses of perturbations of black holes. He combined remarkable insight and calculational ability to develop techniques based on gauge invariant variables that both simplified the calculations and clarified their physical significance. These methods have proven invaluable for subsequent analytic and numerical studies (by Vince and by many others) of black hole stability and gravitational radiation from perturbed black holes.
While a significant portion of Vince's earliest work concentrated on black hole systems, from around 1980 on, Vince's focus has been on cosmological spacetimes. He has shown that large families of them have Cauchy horizons (and therefore violate causality), and has also provided strong evidence that these horizons are absent in generic cosmological spacetimes. He has retrieved from widespread neglect the Belinsky-Khalatnikov-Lifschitz (BKL) conjecture that generic cosmological solutions have either localized Kasner-like or localized mixmaster-like behaviour in the neighbourhood of a cosmological singularity, and then, using both numerical and analytic tools, he has made this idea a dominant theme in the study of the behaviour of cosmological solutions near their singular regions.
Much of the study of cosmological solutions to date has relied on families of spacetimes which have one or two Killing vector fields. It is largely through Vince's systematic study of foliations and gauge choices for these families that they have become efficient mathematical model laboratories for the study of solutions of Einstein's equations. Very recent work of his also points the way to graduating from these restricted faimilies to take on the set of general solutions.
A fair portion of Vince's work throughout his career has been collaborative. This is not surprising, since Vince is a wonderful collaborator. Working with Vince usually involves three stages: first, there is extensive discussion. Ideas get tossed up, get shot down, and get resurrected, all the while filling both the air and many blackboards. Next, there is extensive calculation and checking of arguments. The record of Vince's calculations and arguments is always a big stack of yellow legal-sized sheets of paper, filled with carefully explained and ultra-carefully performed computation and argument. In appearance, these pages are marked by numerous crossed-out terms and equations. Sometimes entire pages get crossed out. However, neither of us can remember ever finding on any of those pages a calculational mistake (even the signs are right!). After this stage is complete, the work gets written up. Vince's portion of the writing appears on those same yellow legal pages. The advent of computers and TeX has not changed this, and likely never will.
Although Vince's research efforts are usually focused on problems that can be tackled using mathematical analysis, he has had a pronounced influence on numerical studies in general relativity. Part of this is the result of his extensive numerical studies of cosmological spacetimes. Equally important is the mathematical work he has done on the constraint equations and on choices of gauge; these set the stage for efficient numerical investigations of gravitational systems. In addition, Vince's influence on numerical relativity is felt through the work of his students, including that of Ed Seidel and Roger Ove.
While most of Vince's work deals with questions arising in classical physics, he has throughout his career thought deeply about quantum physics as well. This interest, in addition to leading to early work on quantized gravitational perturbations and quantum linearization stabilities and to later work on explicit solutions of the Wheeler-DeWitt equation, has been an important motivation for Vince's extensive studies of Hamiltonian reduction of the Einstein system to its true degrees of freedom.
One of the bonuses of a successful scientific research career is the opportunity for travel to many corners of the world. In Vince's case, one of those corners has been Africa. Originally visiting there about ten years ago to serve as a reader for a PhD student in Cameroon, Vince quickly fell in love with Africa. He has become an ardent big game hunter, and visits roughly every year to go on safari in such places as Zimbabwe, Cameroon and Tanzania. In many ways, Vince's great success on African safari mirrors his spectacular success on spacetime safari. We can read about his African safaris at the website http://pantheon.yale.edu/~vem3/safari to learn the details of how he came to have this exotic interest. To read about Vince's spacetime safaris, there is no better source than in his papers.
Vince has told his friends that his most recent African safari may be his last. Whether this is true or not, it is clear that Vince has many exciting spacetime safaris ahead of him. We look forward to hearing about them.
In this volume, we have collected contributions from Vince's collaborators, students and colleagues with similar interests. We hope that, in reading them, you will gain some appreciation of the topics Vince has studied, the contributions he has made, and some of the people who have enjoyed working with him.
Finally, we would like to thank Andrew Wray of IOPP whose encouragement, advice and, most of all, patience enabled the completion of this volume.
Berger Beverly
Isenberg James
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