Scientists at Penn State have reached a new milestone in the effort to model two orbiting black holes, an event expected to spawn strong gravitational waves.

"We have discovered a way to model numerically, for the first time, one orbit of two inspiraling black holes," says Bernd Bruegmann, Associate Professor of Physics and a researcher at Penn State's Institute for Gravitational Physics and Geometry.

Bruegmann's research is part of a world-wide endeavor to catch the first gravity wave in the act of rolling over the Earth.

Computer modeling shows the black hole binary after about one orbit. The black surfaces represent the black holes; whatever falls behind this black hole "horizon" can never escape again. The colored plane shows a measure for the distortion of spacetime. Credit: Bruegmann, Tichy, Jansen 2004 Download larger image version here

A paper describing these simulations will be published in the 28 May 2004 issue of the journal Physical Review Letters. The paper is authored by Bruegmann and two postdoctoral scholars in his group at Penn State, Nina Jansen and Wolfgang Tichy.

Black holes are described by Einstein's theory of general relativity, which gives a highly accurate description of the gravitational interaction. However, Einstein's equations are complicated and notoriously hard to solve even numerically. Furthermore, black holes pose their very own problems. Inside each black hole lurks what is known as a space-time singularity. Any object coming too close will be pulled to the center of the black hole without any chance to escape again, and it will experience enormous gravitational forces that rip it apart.

"When we model these extreme conditions on the computer, we find that the black holes want to devour and to tear apart the numerical grid of points that we use to approximate the black holes," Bruegmann says. "A single black hole is already difficult to model, but two black holes in the final stages of their inspiral are vastly more difficult because of the highly non-linear dynamics of Einstein's theory." Computer simulations of black hole binaries tend to go unstable and crash after a finite time, which used to be significantly shorter than the time required for one orbit.

"The technique we have developed is based on a grid that moves along with the black holes, minimizing their motion and distortion, and buying us enough time for them to complete one spiraling orbit around each other before the computer simulation crashes," Bruegmann says. He offers an analogy to illustrate the "co-moving grid" strategy: "If you are standing outside a carousel and you want to watch one person, you have to keep moving your head to keep watching him as he circles. But if you are standing on the carousel, you have to look in only one direction because that person no longer moves in relation to you, although you both are going around in circles."

The construction of a co-moving grid is an important innovation of Bruegmann's work. While not a new idea to physicists, it is a challenge to make it work with two black holes. The researchers also added a feedback mechanism to make adjustments dynamically as the black holes evolve. The result is an elaborate scheme that actually works for two black holes for about one orbit of the spiraling motion.

"While modelling black hole interactions and gravitational waves is a very difficult project, Professor Bruegmann's result gives a good view of how we may finally succeed in this simulation effort," says Richard Matzner, Professor at the University of Texas at Austin and principal investigator of the National Science Foundation's former Binary Black Hole Grand Challenge Alliance that laid much of the groundwork for numerical relativity in the 90's.

Abhay Ashtekar, Eberly Professor of Physics and Director of the Institute for Gravitational Physics and Geometry, adds, "The recent simulation of Professor Bruegmann's group is a landmark because it opens the door to performing numerical analysis of a variety of black hole collisions which are among the most interesting events for gravitational wave astronomy."

This research was funded by grants from the National Science Foundation including one to the Frontier Center for Gravitational Wave Physics established by the National Science Foundation in the Penn State Institute for Gravitational Physics and Geometry.

Background information

To predict the motion of two black holes is one of the fundamental open problems in general relativity. "Einstein gave us his beautiful theory of general relativity in 1915, and it remains an almost perfect description of the gravitational interaction even by today's standards," Bruegmann says. "But a century later we are still trying to puzzle out how something as simple as the motion of two bodies works in detail." For everyday life and even for most observations in our solar system, the theory of general relativity only adds exceedingly tiny corrections to its precursor, Newton's theory of gravity. Newton's gravity predicts, for example, the Kepler ellipses for the motion of a planet around the sun, which is the classical example for a gravitational two-body problem.

In Einstein's gravity, however, orbital motions produce gravitational waves that carry away energy from the binary system, and the stable, elliptical Kepler orbits turn into slowly decaying, inward spiraling orbits. This basic prediction of general relativity is quite well understood when the motions of the two bodies are not too relativistic. However, the challenge is to compute in the regime of extremely strong and highly dynamic gravitational fields as are present between two black holes shortly before they collide and merge, when their orbits churn up the fabric of space and time and huge amounts of gravitational radiation are produced.