Evolution and Structure of the Universe Ripples In Space And Time
Extending simulation of protein on water 100 times longer than prior work offers new insight.
Ripple in still water
where there is no pebble tossed
nor wind to blow.

— The Grateful Dead

In 1915 Albert Einstein made big waves in physics by propounding a radically new way to think about space, time and gravity. His idea, the general theory of relativity, sent ripples churning through 20th century understanding of the universe that led physicists to the big bang, black holes and brave new worlds of unified theory that reach to embrace all of physics.

Among the still rippling effects of general relativity is Einstein's prediction that moving objects give off gravitational waves. Much like vibrating electrons give off electromagnetic radiation, which allows us to listen to radio and watch TV, the accelerating movements of massive objects in space, such as supernova explosions and black holes, produce gravitational radiation, according to Einstein — ripples moving at the speed of light through the four-dimensional fabric of spacetime.

Important evidence that Einstein was right about gravity waves came from precise measurements of two neutron stars orbiting each other — work which won the 1993 Nobel Prize in physics; the gradual inspiral of the orbits agrees with general relativity theory's predictions for the energy loss that would occur from gravitational radiation. Still, compared to other kinds of radiation, gravity waves are weak, notoriously difficult to detect, and proof of their existence remains a matter of circumstantial evidence.

Ligo Laboratories in Hanford, WA (top) and Livingston, LA.

To clinch the case, scientists at Caltech and MIT, with funding from the National Science Foundation, are building LIGO, the Laser Interferometer Gravitational-Wave Observatory. LIGO's ability to detect gravity waves sometime early in the next century depends critically on a team of University of Pittsburgh physicists. As part of the NSF's Binary Black Hole Grand Challenge Alliance, astrophysicist Jeffrey Winicour and his coworkers are developing computational tools to simulate how black holes emit gravity waves, and in particular gravity waves from two black holes orbiting each other — a binary black hole.

"Calculating the waveforms from the inspiral and merger of binary black holes is important to the success of LIGO," says Winicour, "and it's the prime goal of the Grand Challenge." In late 1997, their computations on the CRAY C90 at Pittsburgh Supercomputing Center marked a milestone along the path toward their goal. Using an innovative new approach, they carried out the first stable, 3D simulations of a single black hole moving through space over a long period of time — an objective that physicists ten years ago saw as "the Holy Grail of numerical relativity."

Gravity Wave from a Moving Black Hole: A snapshot of the gravitational wave scattering from a moving black hole, as simulated by Winicour and his coworkers. The singularity is excised from the numerical integration. The vertical axis corresponds to amplitude of the gravitational field. The horizontal axis represents radial distance. Light can't escape from the region (black) inside the
Gravity Wave from a Moving Black Hole
A snapshot of the gravitational wave scattering from a moving black hole, as simulated by Winicour and his coworkers. The singularity is excised from the numerical integration. The vertical axis corresponds to amplitude of the gravitational field. The horizontal axis represents radial distance. Light can't escape from the region (black) inside the "event horizon" of the black hole.
Download larger version (53KB) of this image.

Getting to the Holy Grail

Even with LIGO, finding gravity waves is something like the proverbial needle in a haystack, except not only don't you know where to look, but the needle, for all you know, looks like a piece of hay. The job of Winicour's group is to provide reliable pictures of the needle. With accurate knowledge of the frequency and amplitude of gravity waves, the LIGO task will be like tuning in a very weak radio signal. "In initial stages," says Winicour, "the signal will be less than the noise due to vibration and other effects, and the more you know about the signal, the better chance you have of detecting it."

Binary black holes are especially important because their gravity waves, according to theory, should be about 100 times stronger than from a single black hole. "It goes on for a longer time," notes Winicour, "and it has a characteristic quasi-periodic frequency, and it just emits more radiation. This is the radiation that LIGO has a good chance of seeing."

To simulate a binary black hole, however, is much more complicated than a single black hole. Even for a single black hole with 3D realism, simulation of its spin and motion was out of range until the Winicour team's breakthrough. This is because general relativity presents an extreme challenge to computational capability. To begin with, a black hole defies mathematics; it contains a point of infinite spacetime curvature and infinite density. Mathematically, such a point is called a singularity. Simulating the physical extremes at such points leads to a problem called numerical instability — the computer program will crash if it attempts to compute near the singularity, and this is the main reason simulating black holes has been impossible till now.

Winicour's team has solved the singularity problem by creating a software module that, in effect, explores the black hole, looking for the singularity and cutting it out of the computation. "Our code locates the black hole," says Winicour, "and then on the fly excises this region inside the black hole as it's moving. You don't lose any of the physics we're interested in, because nothing can get out of that region anyway. Cutting it out allows you to evolve the outside while avoiding this problem with the singularity."

Matching Scheme for Binary Black Hole: Winicour's group is testing this matching scheme as an approach to simulating two orbiting black holes. The retarded time evolution is applied to the region outside G and the regions inside G1 and G2, while standard time is applied to the region in between.
Matching Scheme for Binary Black Hole
Winicour's group is testing this matching scheme as an approach to simulating two orbiting black holes. The retarded time evolution is applied to the region outside and the regions inside 1 and 2, while standard time is applied to the region in between.
Download larger version (11KB) of this image.

Riding the Waves

The Winicour group's recent computations also reflect the success of a new approach they developed for following how a black hole evolves. The standard method — the only method until their work — was to recompute the properties of the spacetime field at succeeding slices of time, going forward in timesteps much like a computation tracking the trajectory of a particle in space. This method presented serious numerical problems due to the strong, rapid fluctuations of gravity waves, especially near the singularity, and it had not been possible to simulate even a single moving black hole in 3D over a long time span.

To overcome this problem, Winicour's team used a different method for labeling points in spacetime, an approach that's based not on standard time but on how light spreads from a point in space — a concept referred to as a light cone. This new approach, called retarded time evolution, smoothes out the irregularities. "With this method, you're not trying to evolve something that's changing very rapidly," explains Winicour. "You go out along the light cone, and it's something like riding with the waves. You smooth out the physical properties quite a bit."

The 1999 Metropolis Award
For his work on this project, Luis Lehner received the 1999 Nicholas Metropolis Award from the American Physical Society. With Winicour as his advisor, Lehner completed his Ph.D. in physics at the University of Pittsburgh in 1998. The Metropolis Award, which honors outstanding doctoral thesis work in computational physics, recognized Lehner's dissertation elaborating retarded time evolution. The award cited Lehner and Winicour as advisor for "developing a method that significantly advances the capability for modeling gravitational radiation by making possible the stable numerical solution of Einstein's equation near moving black holes."

With the success of the retarded time approach, Winicour's team has solved the numerical problems of single black holes. "We can do all the physics of a single black hole spacetime," says Winicour. While this is a major step forward, no one understands better than Winicour the serious work ahead on the path to meeting the goal of LIGO: "The problem of simulating the whole system of a binary black hole has to be broken into regions — some regions far from the hole, some close to the hole, some intermediate regions. Our approach works flawlessly in the far region and the near region, but it breaks down in the region between two holes."

It's a problem with how to label the points for two, as opposed to one, set of light cones. "There's no good way to center your light cones," notes Winicour. "The question is where do you put the origin. The region between has to be done by the standard time approach, and that's still running into instabilities." Full simulation of binary black holes will require melding the two types of time evolution, which the group is working on now.

Pioneering in Spacetime

LIGO is a pioneering effort in modern science, and it's expected to open a new way of viewing the universe. "Once you get past the first detection," says Winicour, "you will have made this major confirmation of a theory of physics. You'll then have a whole new window on astronomy, just like radio astronomy when it came out. It allowed people to see things we weren't aware of."

Up till now, evidence for black holes — like gravity waves — relies on indirect inference. LIGO should firmly verify that black holes exist, and test the predictions of general relativity about the violent spacetime pulsations that accompany black hole collisions. Gravity wave detectors should also tell us more about neutron stars, and how they're born in the explosion of a supernova. They may also give us a look at the instant of the big bang, when space and time came into being. The tools that Winicour's team of numerical physicists are developing, along with the resources of centers like PSC that make their work possible, will play a vital role in this work.

** **
Head-on Collision of Two Black Holes
These images show graphical representation of an axisymmetric, head-to-head collision of two black holes of equal mass and dimension from a time-reversed point of view. In this form, the images show axisymmetric fission of a "white hole" into two white holes. The vertical axis represents time. The closeup looking down from the top of the point of separation shows the verge of bifurcation, where the light rays at opposite poles are about to cross.

Animations can be found here: http://artemis.phyast.pitt.edu/animations/

Researchers: Jeffrey Winicour, University of Pittsburgh.
Hardware: CRAY C90
Software: User developed code.
Related Material on the Web:
Black Hole Grand Challenge Alliance
LIGO — Laser Interferometer Gravitational-Wave Observatory
Pittsburgh Relativity Group
Gravitational Physics Program at the National Science Foundation.
Projects in Scientific Computing, PSC's annual research report.

References, Acknowledgements & Credits

© Pittsburgh Supercomputing Center (PSC)
Revised: August 21, 1998

URL: http://www.psc.edu/science/Winicour/winicour.html