In about five years, the LIGOs should be operational. And they will attempt to experimentally measure-- for the first time--the gravitational waves predicted by Einstein's theory of general relativity. Such a breakthrough would help prove that Einstein's theory of gravity is correct.

The LIGOs will be two of the most sensitive measuring instruments ever built--able to detect variations in the Earth's gravitational field on the order of one one-millionth of a nuclear radius over 1 meter. This would be like measuring a variation of one angstrom in the distance from the Earth to the Sun.

"Gravitational waves should also tell us a lot about astrophysics," says Seidel. "The waves respond to the bulk motion of a large amount of mass. The coherent bulk motion of two stars coalescing or of a nonspher-ical supernova blowing up will yield a wave form that is the only indicator of what the sum of that mass is doing. Currently nothing provides us with information about this 'big picture.' For example, electromagnetic radiation comes from a small local unit like a molecule, but the gravitational wave comes from the global mass. A whole new field of science could spring up around the interpretation of gravitational waves."

"I expect that once LIGO is operational there will be some wave forms detected that we can't explain," says Seidel. "Once we're able to solve Einstein's equations, we should be able to go back and figure out, from a theoretical point of view, what the source of that wave is."

The animation illustrates that black holes seek to maintain a spherical apparent horizon and that two colliding black holes will quickly coalesce into one stable black hole. It also shows that both one- and two-hole systems will oscillate with a mass-dependent resonant frequency.

"Most systems have a normal mode frequency," says Seidel, "just like a bell. If you hit a bell, it rings with a certain frequency. Different sized bells have different frequencies. Black holes also have special frequencies--only the wave being propagated is a gravitational wave."

Seidel's group chose the SGI 360VGX system to produce the video because of its power and built-in animation capabilities. "SGI's VGX was the best machine for making our animation because its built-in graphics hardware and software make it very fast," says Seidel.

The 360VGX contains six RISC-based MIPS architecture CPUs. It employs 85 proprietary graphics processors contained in four pipelined graphics subsystems. Visual data from the RISC host is processed by these subsystems before being displayed on the screen, and parallelism is exploited extensively throughout the system.

Says Seidel, "For the two-black hole system, we can calculate the beginning wave form using an approximation of Einstein's theory or even Newton's laws. And we can calculate the ending wave form after the two have collided using perturbation theory. But there is no easy way to calculate what happens as they approach one another and interact. Here we need a supercomputer because we have to solve the full Einstein equations with no approximations. Our group has made a great deal of progress on the two-black hole collision when it occurs head-on, because then the problem is axisym-metric."

A solution to the full dynamic 3-space Einstein equations is still out of reach. But a recent visitor, graduate research associate Joan Masso from Spain's Universitat de les Illes Balears, developed a promising new approach to the equations that may help realize this goal.

"Masso's approach lets us take well-developed hydrodynamic numerical techniques and apply them to the Einstein equations," says Seidel. "Unfortunately you do give up something with this method, and we're trying to figure out a way to minimize it. The time coordinate necessary for this method to work allows you to get very close to the black hole. And that's bad numerically, because you want to stay away from anything where the numbers are becoming infinite when using a computer. Their system of equations depends crucially on this time coordinate. So we want to figure out a way to avoid the singularity and still use their time slicing division. We are currently working with Masso and also with Wai-Mo Suen at Washington University in St. Louis on a new approach to avoiding singularities. If we can do that, then their form of the equations could definitely improve the numerical solution to the Einstein equations."

Next year Masso may return to NCSA as a postdoctoral visitor and continue work on his techniques.

"One thing we would like to do," says Seidel, "is generate a solver for the Einstein equations and some kind of interface through Mathematica or some other symbolic manipulator. That way, someone working on exact solutions of the Einstein equations using purely analytic techniques could look at our solution and explore the analytic behavior of it."

"Just think what would happen once we develop the technology to solve the general Einstein equations. The knowledge about these equations could just explode--especially if we made it possible for people used to pursuing analytic solutions to take their symbolic manipulators and look at one of our solutions. And when I say 'our' solutions, I'm referring to solutions generated by our group or by those of our collaborators and colleagues at other institutions--such as the University of Texas, the University of North Carolina, Cornell University, the University of Pittsburgh, and Northwestern University, among others. These research groups are planning to work together to develop a solution for the general Einstein equations since this is such a difficult Grand Challenge problem."