Colliding Black Holes: Mathematical Issues in Numerical Relativity
Colliding Black Holes: Mathematical Issues in Numerical Relativity
An ITP Miniprogram, January 10-28, 2000
Overview
Intensive efforts have been underway for the past five years to
numerically calculate the process of the collision and coalescence of two
black holes in general relativity. This problem is of considerable
theoretical interest in its own right, and also is of great importance for
predicting the waveforms for the gravitational radiation signal that LIGO
might detect from this process. In the U.S., the efforts were primarily
undertaken by a Grand Challenge collaboration, but the funding for
this unified collaboration has now expired. However, work continues at a
vigorous pace in a number of groups in the U.S. and elsewhere---most
notably in the Cactus collaboration, a worldwide collaboration
centered at the Albert Einstein Institute in Potsdam, Germany.
There has been relatively little interaction between the numerical
relativists carrying out this research program and mathematically
oriented general relativists. Yet, a number of issues have arisen where
further input from mathematical general relativists might be of great use.
One example of such an issue is the form in which Einstein's equation is
expressed: Do hyperbolic formulations have advantages over non-hyperbolic
formulations? If so, which hyperbolic formulations are "best"? Another
major issue involves the choice of coordinate and time slicing conditions:
If one chooses a slicing so as to avoid the physical singularities
produced by the collapse, severe "grid stretching" difficulties arise.
These are presently being dealt with by excising the black hole from the
spacetime, but present procedures remain rather rudimentary and
undeveloped.
The goal of this miniprogram is be to bring together numerical relativists and
mathematical general relativists to discuss these and other issues related to the
black hole collision problem.
Participants
Schedule
Please send mail to Matt Choptuik to report problems/errors with the schedule, or
to volunteer to speak, or to suggest specific topics for Discussion Sessions.
Monday January 10
| 8:30 |
| Registration |
| 9:00 | Gross | Welcome to the ITP |
| 9:15 | Choptuik, Seidel & York | Welcome to the Miniprogram |
| 9:30 |
| Coffee/ITP Orientation/Organization |
| 10:00 | Smarr | The First 50 Years of the Two BH Collision Problem: 1935 to 1985 |
| 11:15 | Wald | Horizons |
| 12:00 |
| Lunch |
| 2:00 | Baumgarte, Cook, Kidder & Scheel | Cornell/NSCA-3+1 Group Report |
| 4:00 |
| Coffee/Cookies/Discussion |
| 7:00 |
| Dinner |
Tuesday January 11
| 8:30 |
| Discussion/Coffee |
| 9:30 | Alcubierre, Bruegmann & Seidel | Potsdam-3+1 Group Report |
| 11:00 |
| Discussion/Coffee |
| 12:00 |
| Lunch |
| 2:00 | Baumgarte, York, Lehner & Gomez | Equations of Motion |
| 4:00 | Smarr | Physics Dept. Colloquium |
| 7:00 |
| Dinner |
Wednesday January 12
| 9:00 |
| Discussion |
| 9:30 | Huq & Lehner | Texas/Penn State/Pitt-3+1 Group Report |
| 11:00 |
| Discussion/Coffee |
| 12:00 |
| Lunch |
| 2:00 | Friedrich | Outer Boundaries: Problems and Solutions |
| 3:30 | Szilagyi | Cauchy Boundaries in Linearized Gravitational Theory |
| 4:00 |
| Coffee/Cookies/Discussion |
| 7:00 |
| Dinner |
Thursday January 13
| 8:30 |
| Discussion/Coffee |
| 9:00 | Damour | Analytical Approach to the Coalescence of Two Black Holes (Summary) |
| 9:30 | Gomez & Lehner | Pittsburgh-Null Group Report |
| 11:00 |
| Discussion/Coffee |
| 12:00 |
| Lunch |
| 2:00 | Huebner | Potsdam-Conformal Group Report |
| 3:30 |
| Coffee |
| 4:00-6:00 | Gundlach, Garfinkle, Moncrief, Eardley | Coordinate Conditions |
| 7:00 |
| Dinner |
Friday January 14
| 8:30 |
| Discussion/Coffee |
| 9:30 | Shapiro & Shibata | 3D Numerical Relativity: Preview of Astrophysical Payoff & 3D General Relativistic Hydrodynamics |
| 11:00 |
| Coffee |
| 11:30 | Suen & Miller | NASA Neutron Star Grand Challenge Project & the NSF Astrophysics Simulation Collaboratory Project |
| 12:45 |
| Pizza Lunch and Discussion |
| 2:00 | Wald et al | Planning Session for Future Program(s) |
| 2:30 | Bruegmann & Huq | Black Hole Excision & Apparent Horizons |
| 4:30 |
| Coffee/Planning Session |
| 7:00 |
| Dinner |
Monday January 17
| Martin Luther King Day | ITP/USCB closed |
Tuesday January 18
| 10:00 | Misner | Models of Steady State Radiation Computation |
| 12:00 |
| Lunch |
| 2:00 | Kashif, Goncalves & Thorne | Issues in the IBBH Problem |
Wednesday January 19
| 10:00 | Damour | Analytical Approach to the Coalescence of Two Black Holes |
| 12:00 |
| Lunch |
| 2:00 | Ashtekar | Mass and Angular Momentum of Isolated Horizons |
| 3:45 | Isenberg | Gluing Solutions of the Constraints |
Thursday January 20
| 10:00 | Garfinkle | Axisymmetric Simulation of Brill Waves |
| 12:00 |
| Lunch |
| 2:00 | Eardley et al | General Discussion |
Friday January 21
| 10:00 | O'Murchadha | Collapse of the Lapse in Harmonic Gauge |
| 12:00 |
| Lunch |
Monday January 24
| 10:00 | Berger | Exploring "Mathematical Cosmology" With Numerical Simulations |
| 12:00 |
| Lunch |
Tuesday January 25
| 10:00 | Moncrief | Conformally Regular ADM Evolution Equations |
| 12:00 |
| Lunch |
Wednesday January 26
| 10:00 | Bardeen | Comparing Hyperbolic Methods, Gauge Conditions, and Boundary Conditions for the Non-linear Plane Wave |
| 12:00 |
| Lunch |
Thursday January 27
| 10:00 | Rendall | Hyperbolicity in Numerical Relativity |
| 12:00 |
| Lunch |
Friday January 28
| 12:00 |
| Lunch |
| 2:00 |
| Program wrap up |
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The Institute for Theoretical Physics
Kohn Hall, UC Santa Barbara,
Santa Barbara, CA 93106
(805) 893-4111
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 ITP is funded by
National Science Foundation
and by the
University of California
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