Numerical Relativity (05w5087)
Douglas Arnold (University of Minnesota)
Matthew Choptuik (University of British Columbia)
Randy LeVeque (University of Washington)
Eitan Tadmor (University of Maryland)
Many groups around the world have been working intensively on numerical relativity for the past several years, and yet progress has been slow due to a variety of numerical and analytical difficulties. There are many potential opportunities for numerical analysts and other applied mathematicians to share expertise gained in other fields and find new problems to tackle, which may lead to the development of new mathematical and computational techniques. An increasing number of mathematicians are starting to work in this area. However, there is a steep learning curve that is an impediment to getting started in this field and it is essential that mathematicians have an opportunity to work directly with knowledgeable physicists who have expertise in general relativity and first-hand experience with the mathematical and numerical difficulties encountered. Conversely, applied mathematicians collectively have a broad knowledge of techniques that have been developed in other computational sciences and that may be applicable in numerical relativity.
The primary goal of this workshop is to provide an opportunity for small group of physicists and mathematicians interested in numerical relativity to come together in an intimate atmosphere and share their expertise. We plan to invite people who we are truly interested in communicating in this manner. We will have a small number of talks that are aimed at educating others rather than presentation of people's latest results. Ample time will be left for informal discussion and we believe that the facilities at BIRS are ideally suited to such a workshop.
A similar workshop was held at the IMA in June, 2002; see http://www.ima.umn.edu/nr/ Four of the current organizers attended that workshop (Doug Arnold was one of the organizers), and experiences from that workshop will be used as a guide to planning this one. It was generally felt that the IMA workshop was extremely valuable and that more workshops of this nature are needed. A BIRS workshop in 2005 would be an excellent opportunity to reinforce some of the interactions forged at the IMA and to generate new ones by involving a different, though overlapping, set of researchers.
We plan to invite 10-15 numerical relativists, an equal number of mathematicians, and 8-10 junior researchers (PhD students or postdocs from either discipline) who are starting to work in numerical relativity and who could also greatly benefit from this forum.
Interest in numerical relativity has been bolstered by the recent construction of gravitational wave observatories such as LIGO (the Laser Interferometric Gravitational-wave Observatory). This NSF-supported project consists of two observatories (near Hanford, Washington and Livingston, Louisiana) that began collecting data in September, 2002. Astronomy has been revolutionized in the past by developing the ability to observe electromagnetic radiation in new wavelength regimes (e.g., by X-ray and radio telescopes). If successful, the development of gravitational-wave observatories will surely lead to many new surprises. However, gravitational waves reaching earth are incredibly weak and have yet to be detected. Being able to predict the gravitational wave signature of various possible events would help interpret any data received and separate the weak signal from noise.
Furthermore, the Einstein equations represent one of the richest and most difficult systems of PDEs describing a viable physical theory. Simulations will play a crucial role in understanding these equations, particularly since experiments cannot be performed. To date, most of what is known about solutions of these equations has been obtained from different approximations that limit the nature of solutions found. Numerical simulations have the potential for unraveling the full consequences of the theory and robust implementations of the equations will certainly give rise to surprises. For instance, the discovery of black hole ``critical pheonemena'' highlighted the fact that fascinating effects can be revealed through carefully constructed simulations. The planned workshop will bring together researchers from numerical relativity and mathematics in order to improve the chance that the full potential of numerical relativity is achieved sooner rather than later.