Blackhole Einsteins's

Black hole studies to verify Einstein's theory

by Randall Graham, Science Writer
Recent government approval to fund construction of two Laser Interferometric Gravi-tational Wave Observatories (LIGOs) has increased the urgency with which NCSA research scientist Ed Seidel and his NCSA colleagues (Peter Anninos, David Bernstein, Steve Brandt, Karen Camarda, Larry Smarr, and John Towns) are seeking to define the gravitational wave signatures of black holes via theory. If LIGO researchers are to tell true gravitational waves from false readings, the signatures are important.

In about five years, the LIGOs should be operational. And they will attempt to experimentally measure-- for the first time--the gravitational waves predicted by Einstein's theory of general relativity. Such a breakthrough would help prove that Einstein's theory of gravity is correct.

The LIGOs will be two of the most sensitive measuring instruments ever built--able to detect variations in the Earth's gravitational field on the order of one one-millionth of a nuclear radius over 1 meter. This would be like measuring a variation of one angstrom in the distance from the Earth to the Sun.

Einstein's gravity

Einstein's theory of general relativity defines gravity as variations in the curvature of spacetime and predicts that cataclysmic astrophysical events, such as exploding supernovas or colliding black holes, send gravitational waves rippling through the curved geometry of the universe. Although they are very weak, the waves should create a detectable gravitational disturbance as they pass Earth. Each type of phenomenon should generate a unique wave signature that scientists can decipher to trace the source.

"Gravitational waves should also tell us a lot about astrophysics," says Seidel. "The waves respond to the bulk motion of a large amount of mass. The coherent bulk motion of two stars coalescing or of a nonspher-ical supernova blowing up will yield a wave form that is the only indicator of what the sum of that mass is doing. Currently nothing provides us with information about this 'big picture.' For example, electromagnetic radiation comes from a small local unit like a molecule, but the gravitational wave comes from the global mass. A whole new field of science could spring up around the interpretation of gravitational waves."

Developing a gravitational wave catalog

One of Seidel's goals is to use super-computers to provide part of a wave signature catalog for LIGO researchers to help them recognize the sources of detected waves. At the same time, the theoretical framework developed in making the catalog should provide researchers with a means of tracing unknown LIGO signatures in the future.

"I expect that once LIGO is operational there will be some wave forms detected that we can't explain," says Seidel. "Once we're able to solve Einstein's equations, we should be able to go back and figure out, from a theoretical point of view, what the source of that wave is."

Understanding black hole resonance

Recently Seidel and his colleagues created an animation of one- and two- black hole systems using the Silicon Graphics VGX system. The video shows the evolution of apparent black hole horizons in settings where the holes are distorted initially and then allowed to snap back to their stable, equilibrium state. (The apparent horizon is defined as a mathematical boundary surrounding a black hole at which outgoing light rays are trapped and are no longer expanding away from the hole.)

The animation illustrates that black holes seek to maintain a spherical apparent horizon and that two colliding black holes will quickly coalesce into one stable black hole. It also shows that both one- and two-hole systems will oscillate with a mass-dependent resonant frequency.

"Most systems have a normal mode frequency," says Seidel, "just like a bell. If you hit a bell, it rings with a certain frequency. Different sized bells have different frequencies. Black holes also have special frequencies--only the wave being propagated is a gravitational wave."

Seidel's group chose the SGI 360VGX system to produce the video because of its power and built-in animation capabilities. "SGI's VGX was the best machine for making our animation because its built-in graphics hardware and software make it very fast," says Seidel.

The 360VGX contains six RISC-based MIPS architecture CPUs. It employs 85 proprietary graphics processors contained in four pipelined graphics subsystems. Visual data from the RISC host is processed by these subsystems before being displayed on the screen, and parallelism is exploited extensively throughout the system.

Searching for a missing part of the two-hole wave form

For some time scientists have understood the wave form for two black hole systems during two stages: when the holes are far apart and after they have collided. NCSA Director Smarr's Ph.D. thesis in 1975 was dedicated to building the computing and theoretical understanding of what happens as the two holes approach and influence one another.

Says Seidel, "For the two-black hole system, we can calculate the beginning wave form using an approximation of Einstein's theory or even Newton's laws. And we can calculate the ending wave form after the two have collided using perturbation theory. But there is no easy way to calculate what happens as they approach one another and interact. Here we need a supercomputer because we have to solve the full Einstein equations with no approximations. Our group has made a great deal of progress on the two-black hole collision when it occurs head-on, because then the problem is axisym-metric."

A solution to the full dynamic 3-space Einstein equations is still out of reach. But a recent visitor, graduate research associate Joan Masso from Spain's Universitat de les Illes Balears, developed a promising new approach to the equations that may help realize this goal.

A new, easier way to write Einstein's full equations

Masso and his advisor, Carles Bona, came up with a new way of writing the general Einstein equations in a flux conservative form. It's a form that allows one to use techniques for solving hydrodynamic equations and apply them to Einstein's equations for the first time.

"Masso's approach lets us take well-developed hydrodynamic numerical techniques and apply them to the Einstein equations," says Seidel. "Unfortunately you do give up something with this method, and we're trying to figure out a way to minimize it. The time coordinate necessary for this method to work allows you to get very close to the black hole. And that's bad numerically, because you want to stay away from anything where the numbers are becoming infinite when using a computer. Their system of equations depends crucially on this time coordinate. So we want to figure out a way to avoid the singularity and still use their time slicing division. We are currently working with Masso and also with Wai-Mo Suen at Washington University in St. Louis on a new approach to avoiding singularities. If we can do that, then their form of the equations could definitely improve the numerical solution to the Einstein equations."

Next year Masso may return to NCSA as a postdoctoral visitor and continue work on his techniques.

"One thing we would like to do," says Seidel, "is generate a solver for the Einstein equations and some kind of interface through Mathematica or some other symbolic manipulator. That way, someone working on exact solutions of the Einstein equations using purely analytic techniques could look at our solution and explore the analytic behavior of it."

Solving Einstein's equations: A Grand Challenge

"This whole incredible field of black hole physics has come out of the one solution to Einstein's equations, the Schwarzschild solution. It was developed the year after Einstein's theory was published, and it's a simple spherical solution," Seidel continues.

"Just think what would happen once we develop the technology to solve the general Einstein equations. The knowledge about these equations could just explode--especially if we made it possible for people used to pursuing analytic solutions to take their symbolic manipulators and look at one of our solutions. And when I say 'our' solutions, I'm referring to solutions generated by our group or by those of our collaborators and colleagues at other institutions--such as the University of Texas, the University of North Carolina, Cornell University, the University of Pittsburgh, and Northwestern University, among others. These research groups are planning to work together to develop a solution for the general Einstein equations since this is such a difficult Grand Challenge problem."