# Gravitational Waves: An Illinois Connection

On February 11, the National Science Foundation made an astounding announcement. According to the NSF press release, scientists had for the first time “observed ripples in the fabric of spacetime called gravitational waves, arriving at Earth from a cataclysmic event in the distant universe. This confirms a major prediction of Albert Einstein's 1915 general theory of relativity and opens an unprecedented new window to the cosmos.”

The import of this observation is vast. Einstein’s theory underpins the modern understanding of the universe. Part of this theory predicts that two black holes colliding would create waves of gravitational radiation (gravitational waves). However, detecting these waves on Earth would be extremely difficult because these waves would be extremely small. Ed Seidel, director of the National Center for Supercomputing Applications (NCSA), explained, “Einstein himself did not believe that those waves could ever be detected, if they were even real.”

The detection of these waves just weeks ago by the Laser Interferometer Gravitational-wave Observatory (LIGO) was the culmination of a century of effort by scientists to find evidence that would support Einstein’s equations that stem from his theory of general relativity.

And part of that history took place at the University of Illinois among computer scientists and mathematicians of the Department of Computer Science and NCSA.

In the early 1990s, Seidel was a research scientist at NCSA whose work focused on the problem of solving Einstein’s equations, specifically looking at the black hole and gravitational wave problems presented in those equations. Soon after he arrived, he met CS Professor (now Professor Emeritus) Paul Saylor, whose own research examined how mathematics related to the physical sciences, particularly focusing on partial differential equations and linear algebra. They quickly hit it off and started collaborating on the problem of solving Einstein’s equations.

Saylor was particularly impressed by Seidel and his research. “I was present at many technical discussions by Ed,” Saylor said, “which convinced me that this guy is unbelievable. He knows everything, and I was fortunate to have him to work with.”

One of Saylor’s graduate students, Steven Lee (PhD CS ‘93), was doing his doctoral research on developing equations that were able to conserve certain constraints, such as conservation of mass or of momentum. This work dovetailed nicely with the physics work that Seidel was doing at NCSA. Together with Saylor, Lee met regularly with Seidel’s NCSA team to develop approaches to solving the Einstein equations.

“I worked with Ed’s team on some test problems that they already were starting to have some challenges with and to apply the software that I was developing for my PhD thesis,” said Lee. The computer work that Lee was performing helped to solve some of the problems that Seidel was having on the physics side.

“It was Steve who probably gave Ed the most computational help, because this was his application problem for a PhD in computer science,” Saylor said. “The rest of us tried to make sense out of what Steve was coming up with, which included some of the most elegant algebraic relations I’ve had the good fortune to enjoy.”

Although Saylor would describe his impact on these research endeavors modestly—saying his role ranged “from not too significant to very insignificant”—others would disagree. Seidel said the work Saylor had been doing was important to his research efforts. “Many of the techniques that Paul had developed around linear systems and solving elliptic equations and so on are the kinds of equations that show up in Einstein’s equations,” said Seidel.

In fact Seidel got his first grant with Saylor as the co-principal investigator. “We put the proposal together, and Paul probably wrote the lion’s share of the proposal. I had the physics knowledge, and Paul had the mathematical knowledge of how to solve these kinds of equations,” Seidel said.

“I believe that Paul was instrumental in terms of connecting the dots [for] getting the top computational scientists interested in this problem,” said Lee, noting that these connections developed important interactions across science fields. “It was a new degree of collaborating between mathematicians and computer scientists and physicists—people who were studying general relativity.”

The gravitational waves announced in February were first detected on September 14, 2015, at 5:51 a.m. EDT by both of the twin LIGO detectors located in Livingston, Louisiana, and Hanford, Washington. These waves provided information about their origins and about the nature of gravity that cannot be obtained from elsewhere. Physicists have concluded that the detected gravitational waves were produced during the final fraction of a second of the merger of two black holes to produce a single, more massive spinning black hole. It was this collision that had been predicted through Einstein’s equations, but never observed.

NASA has created a video simulating this event:

The work done at Illinois in the 1990s was early work. These researchers knew that the technology they were dealing with was not yet ready at that time to make the discovery that occurred in February. “This was very much blue sky research,” Lee said. “You didn’t have these gravitational wave reports yet, but we started doing the groundwork on the mathematics and the computational software needed for preliminary studies of what signals we might expect to detect [in the future].”

Following his graduation from Illinois, Lee spent time at Oak Ridge National Laboratory, MIT (as a visiting professor), and then Lawrence Livermore National Laboratory. Today, he continues to work in computational science and applied mathematics research.

“There are now more sophisticated methods,” Seidel explained. “I don’t want to say that they are using the methods that we developed. But we did do—in collaboration with Paul—the first three-dimensional collisions of black holes and wave forms from them. Those were stepping stones along the way. Now there are more modern methods that do an even better job than we could do when we were doing this.”