Making Black Holes Go ‘Round on the Computer

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.

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.

CONTACTS:

Bernd Bruegmann: (+1)814-865-1272, bruegman@gravity.psu.edu or bpb10@psu.edu

Barbara K. Kennedy (PIO): (+1)814-863-4682, science@psu.edu

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.