Albert Einstein was not exaggerating when he said that his gravitational field equations presented ‘very serious’ mathematical difficulties. In fact, it took nearly 90 years from the publication of his paper on general relativity to the first successful solution of the two-body problem: the merger of two black holes. The problem occupied some of the finest minds in mathematics, as well as some of the biggest iron in computing. Even then, the effort to solve these equations has been a long and hard road and not one for the faint-hearted. Many scientists saw numerical relativity as a worthy, but ultimately not the most glamorous, career path.
In fact, three groups published the first solutions almost simultaneously after a breakthrough in the mathematical approach. Since then, numerical relativity has blossomed from the Cinderella of physics to the belle of the ball.
While most of these groups were academic – and doing it for its scientific value – one group in particular had to solve the problem, because it had an appointment in outer space. Joan Centrella leads the theoretical astrophysics team at NASA’s Goddard Space Flight Centre, which was in the leading pack. NASA was interested in the problem, because it has scheduled the $2bn joint US/European Laser Interferometer Space Antenna (LISA) mission. This will send three spacecraft to carry instruments the size of a Chinese takeaway container to stand three million miles apart and look for gravity waves. It’s a fiddly experiment, so it is very important to know what a gravity wave might look like.
Robin Stebbins, NASA project scientist for LISA and in charge of the experimental side, says: ‘Joan has been a major player in recent advances in numerical relativity. Some of the work that Joan and her group have done has suggested that there is a greater richness of events than previously imagined, such as the possibility that a merger might give a big enough kick to the resulting massive black hole to knock it out of the host galaxy.
‘Of course we still know very little about what happens out there, but this suggestion, particularly its velocity, was somewhat shocking and could only have been determined by a full numerical solution.
‘There has been a sub-field of theoretical physics that has laboured at the problem of merging two black holes for 30 to 40 years, but it was largely a demoralising effort. Every time someone seemed to break through one particular set of problems, more problems emerged. So the characteristic of those who came up with the final solution is endurance. Joan has been very shrewd in assembling her team and empowering them to do what they do best, while also co-ordinating them. These computational codes are almost corporate enterprises on their own. You have to bring together a collection of talents and get them playing together; you have to scrabble for resources, and Joan and her group were at the nexus of a lot of things at a moment in history. To take the problem on after so many discouraging results and amass the skillset and resource to overcome the remaining problems was quite an accomplishment.
‘She spends a lot of time fostering a group dynamic in what is a team intellectual activity. She works hard to make sure that the contributions of each member of the team are recognised. As it happens, three groups got to the same point almost simultaneously and, since then, there has been a flood of new results. People then decided what part of the problem they would work on in a kind of land rush, and Joan has been very successful in choosing the areas to which her team can contribute most effectively.
‘Joan is an energetic individual who is excited about what she does, and when she gives talks to groups of people, she transmits her excitement. She would readily admit that she has an active and vigorous personality; collaborating with her is a delightful process. She has very strong principles and, if you want to test them, she is quick to react. Joan will tell you straight away if she is in favour of something or against it.’
Centrella was born in Winsted, a small industrial town in Connecticut. Her mother had worked as a bookkeeper and various other jobs and her father was a machinist. Centrella says: ‘To be honest, I don’t really know what my father did; he worked in a factory. When I was a child, his company got a contract to make a part for an astronaut’s backpack – I have a picture of the backpack on my wall. My father got to work on part of it and he was very proud of this. He took me into the factory after work to show me this thing.
‘I was very taken with NASA when I was a child and I wrote to NASA and they sent me various publications. I collected everything I could find about NASA and kept it in my room. When we were allowed to take our text books home in fourth grade I was so excited, because I could actually read the science book. I got to read about astronomy and, as I found out more about it, I discovered that it was possible to become an astrophysicist. Since then, that is all I wanted to be.’
Centrella was a very good student, doing well in languages and literature as well as maths and science. She spent all her time studying or reading and very little on sports and games. She did well at school and became the first person in her father’s family to go into higher education. She chose the University of Massachusetts partly because it was not far away, but mainly because it allowed her to major in astronomy.
Centrella loved it. She went to every lecture and took reams of notes and then prepared questions with which she bombarded the lecturers. In years to come, when she taught her own courses, she was amazed how few students did the same to her.
She says: ‘The professors were all very agreeable to talking with me. When I later on became a professor, it astonished me that hardly anyone came to “office hours”. I liked lectures, but I really learned the most processing that information with the professor. I thought the reason you went to college was the people. It’s so exciting as a teacher if someone is interested in what you are saying.’
Her undergraduate advisor was distinguished cosmologist Ted Harrison, who encouraged Centrella to apply for a scholarship to an English university. She eventually won a Marshall Scholarship to Cambridge University Institute of Astronomy, where she gained her PhD.
She says: ‘It was a bit of a culture shock, but I had an excellent advisor in Bernard Jones. He gave me a very important gift, which was being able to find out what I really wanted to work on. I had this idea that I really wanted to work on relativity and cosmology. Over a period of time, I found my way into this world of numerical relativity. At this time there had been a lot of work that was analytical, and Larry Smarr, then a post doc at the Center for Astrophysics at Harvard and subsequently at the University of Illinois, was pioneering the numerical approach, which resulted in pressure from the community that this was not the right way to go. Most people in general relativity were theorists, and did not understand or appreciate the importance of numerical simulations to solve Einstein’s equations.
Joan Centrella (left) and her team at the NASA Goddard Space Flight Center: Sean McWilliams, Bernard Kelly, James van Meter, Darian Boggs, and John Baker.
At the time, using computers to create numerical solutions to equations was characterised as ‘brute force’. It was many years before physics accepted these methods, even though meteorologists had been using numerical methods for many years. Centrella had discovered a book called Gravitation, by Charles Misner, Kip Thorne and the legendary physicist John Wheeler, which talked about solving the equations on a computer. Wheeler and Bryce DeWitt had had inspired Smarr’s work. One day Centrella came across a pre-print of one of Smarr’s papers on numerical relativity and this inspired her to learn how to use computers and join the fray.
She says: ‘My supervisor handed me his Fortran manual and told me to get a computer account. I learned how to log in and how to write programmes. I then got a book on how to solve differential equations on a computer, and I think the third programme I ever wrote was a programme to solve Einstein’s equations using Larry Smarr’s pre-print. Larry visited Cambridge the next year and I got to know him. He helped my career quite a bit and later on I became his postdoc.’ Her first post doc position was at the University of Texas in Austin, where she worked with Richard Matzner, whom she first met in Cambridge. She spent a couple of years at the University of Illinois working with Larry Smarr before returning to Texas. She had moved into largescale structure simulations by this time and numerical relativity was on the back burner.
In 1984 she was approached by Drexel University’s department of physics and atmospheric science. Centrella said that the department understood high performance computing and the collegial atmosphere attracted her.
She says: ‘When I went there, everyone knew each other. It was a very friendly place, and I valued that. They wanted to build an astrophysics group and so they hired me and later hired Steve McMillan. They didn’t have great computing facilities of their own, so we used the computers at the NSF centres in San Diego and Illinois by applying for grants. Before the national centres were set up, I used to really scrounge for computer time. I even managed to get some time from Cray Research where I had got to know one of its application specialists. I also got time from a movie production company in Hollywood, which had a Cray computer.’
In the early 1990s, she had started working on gravitational wave signals that might be received by ground-based detectors. At this point the NSF launched its Binary Black Hole Grand Challenge, inviting scientists to simulate the gravity waves that would be detectable by the ground-based project LIGO. Centrella was one of the few scientists in the field not to take part as she was focused on neutron stars.
In 2000 the Decadal Review of Astronomy featured a high ranking for a space borne gravitational detector, so NASA started to take it seriously. It was not on Centrella’s radar screen at the time, but she happened to visit the Goddard Center, just as NASA had been funded to hire relativity scientists to work on the theoretical side of the LISA mission. They offered Centrella the chance to form a numerical relativity group at Goddard to focus on the black hole problem.
She says: ‘Not everyone would make this choice, but for me it was a great opportunity, because at the time they were also hiring an experimental group. The chance to be directly alongside the experimentalists working on all aspects of astrophysical science was very important to me. It was an irresistible offer. People might say “if you go to Goddard, you have to work on LISA”. I say “great, I get to work on LISA”.’
Centrella went from a small private university to a huge government bureaucracy, which was a culture shock, but the scientific work was the same. The upside of being part of a large organisation is that it is mission oriented, and was able to give her all the resources she asked for to build her group, despite the budget pressures.
She says: ‘They gave me what I needed and I was able to hire a group of splendid scientists. I think one of the reasons our group succeeded so well is that we had the mission focus. I felt that being here with the people working on LISA kept us focused on the black hole problem. Had we been at a university, we would have been distracted by other problems.
‘I remember people asking me when I thought we would have this problem solved. I said to them that there were people who believed it was never going to be solved. I told them I believed it was possible and they said they were OK with that, and gave me the resources. They backed me and gave me everything I asked for. We got to use the computers here at Goddard as well as the Columbia machine at the Ames Research Center – where we did our big breakthrough work.’
The problem with numerical relativity was that the system of equations had unstable modes, which would grow and cause the computer to crash. By 2001 a lot of the problems had been sorted out. The problem was that the simulations could not be made to run long enough to get meaningful results. In 2004 a group at Jena published a paper about a simulation that lasted long enough for a single orbit.
Centrella says: ‘This was a wake-up call and everyone realised that the solution might be close. A year later, the first merger was achieved by Frans Pretorious, then at Caltech and the University of Alberta, who used a different technique to resolve the black holes. In late 2005 a group led by Manuela Campanelli at the University of Texas, Brownsville and our group independently came up with a way of handling the black holes and moving them across the grid. Most of the community was using the “puncture method” and it was believed that the punctures had to be fixed in the grid. The Jena group had come up with a clever way of making the black holes orbit. Frans also used a different technique that most people thought would solve the problem. But our group and the Brownsville group independently came up with a way of changing the co-ordinate conditions that worked.
‘In November 2005 we held a workshop at Goddard to debut our work and the Brownsville group presented ahead of us. We discovered that they had come with exactly the same result! It was quite an earth-shaking thing and caused a huge stir. We published back-to-back in Physical Review Letters. Suddenly all those puncture codes out there with a few changes started working. Some people said it would not work, but other people plugged it in and it worked. In April 2006 there was a meeting when the room was overflowing with people who had got results. By the summer everyone was using this method and the field has grown exponentially since then. The landscape has completely changed.’
Centrella says that being part of a government agency has its own challenges, but she believes that her team was never deprived of resources and worked better because of the focus on the mission – even though the launch date has been pushed out to 2018.
She says: ‘I am very glad that I am here, because they gave me the resources to do this fantastic work. Everyone has issues with where they work, but there is a certain thrill I get when I drive onto this facility and see that sign saying “Goddard Space Flight Center”. When I drive past that sign I think “Wow, I work for NASA. How cool is that?”
‘There is something about NASA; the fact that we are dedicated to looking out from the Earth touches people’s hearts and minds in terms of exploration of the future. Here, there is this excitement that is deep within me.
‘On my wall at Goddard I have a picture of an astronaut wearing a backpack that my father worked on all those years ago. To me, that is my roots and I think it is truly wonderful that I could come to NASA and do this work. I am really grateful.’
Education
1975 University of Massachusetts, B.S Astronomy
1980 University of Cambridge Institute of Astronomy, PhD
Employment
1979–81 University of Texas, Austin, post doctoral researcher
1981–83 University of Illinois, post doctoral researcher
1983–84 University of Texas, Austin, lecturer, astronomy department
1984–2001 Drexel University, associate then full professor from 1997
2001–2004 Astrophysicist, Gravitational Astrophysics Laboratory, NASA Goddard Space Flight Center
2004 to date Chief, Gravitational Astrophysics Laboratory, NASA Goddard Space Flight Center