For years scientists trying to visualize the concept of gravitational waves churned by the collision of black holes have relied largely on artists’ conceptions. Now, at long last, they have Einstein’s conception.

According to Einstein, when two massive black holes merge, all of space jiggles like a bowl of Jell-O as gravitational waves race out from the collision at light speed. This is a mind-boggling notion, to be sure.

NASA scientists have reached a breakthrough in computer modeling that allows them to simulate what gravitational waves from merging black holes look like. The three-dimensional simulations are a manifestation of Einstein’s equations, pure and simple. And they are the largest astrophysical calculations ever performed on a NASA supercomputer.

Previous simulations had been plagued by computer crashes; the equations needed, based on Einstein’s general relativity, were far too complex. But scientists at NASA Goddard Space Flight Center in Greenbelt, Md., have found a method to translate Einstein’s math in a way that computers can understand.

The simulations provide the foundation to explore the universe in an entirely new way. You see, there’s more to the universe than what meets the eye.

Our eyes detect light in the optical waveband. Since the dawn of mankind until only about a hundred years ago, this was the only form of "radiation" humans knew. Then scientists discovered radio waves, infrared light, ultraviolet light, X-rays and gamma rays. Suddenly a new window to the universe was open.

Einstein predicted the existence of gravitational radiation. Similar to ripples on a pond, gravitational waves are ripples in space and time, a four-dimensional concept that Einstein called spacetime. They haven’t yet been detected directly.

"These mergers are by far the most powerful events occurring in the universe, with each one generating more energy than all of the stars in the universe combined," said Dr. Joan Centrella, who leads the Gravitational Astrophysics Laboratory at Goddard.

Gravitational waves hardly interact with matter and thus can penetrate the dust and gas that blocks our view of black holes and other objects. The gravitational waves from the big bang itself could still be rolling through the universe.

The National Science Foundation’s ground-based Laser Interferometer Gravitational-Wave Observatory (LIGO) and the proposed Laser Interferometer Space Antenna (LISA), a joint NASA – European Space Agency project, hope to detect these subtle waves, which would alter the shape of a human from head to toe by far less than the width of an atom. This is one of the hottest fields in astronomy, the new (and final?) frontier.

Black hole mergers produce copious gravitational waves, sometimes for years, as the black holes approach each other and collide. Black holes are regions where gravity is so extreme that nothing, not even light, can escape its pull.

Black holes alter spacetime. Therein lies the difficulty in creating black hole models: Space and time shift; density becomes infinite and time can come to a standstill. Such variables cause computer simulations to crash.

These massive, colliding objects produce gravitational waves of differing wavelengths and strengths, depending on the masses involved. The Goddard team has perfected the simulation of merging, equal-mass, non-spinning black holes starting at various positions corresponding to the last two to five orbits before their merger.

With each simulation run, regardless of the starting point, the black holes orbited stably and produced identical waveforms during the infall, collision and aftermath. This was a first. The combination of stability and reproducibility assured the scientists that the simulations were true to Einstein’s equations. The team has since moved on to simulating mergers of non-equal-mass black holes.

The simulations were done on the Columbia supercomputer at NASA Ames Research Center near Mountain View, Calif. Dr. John Baker of NASA Goddard, the lead author on papers about this work in Physical Review Letters and Physical Review D, described the complexity of the simulations.

Einstein’s theory of general relativity employs a type of mathematics called tensor calculus, which cannot be inputted directly into computer coding, Baker explained. The equations need to be translated, which greatly expands them. The simplest tensor calculus equations require thousands of lines of computer coding. The expansions, called formulations, can be written in many ways. Through mathematical intuition, the Goddard team has found the appropriate formulations to lead to suitable simulations.

Progress also has been made independently by several groups, including researchers at the Center for Gravitational Wave Astronomy at the University of Texas at Brownsville.

"These simulations enable us to visualize Einstein’s equations," said Dr. Paul Hertz, Chief Scientist, NASA’s Science Mission Directorate. "Now when we observe a black hole merger with LIGO or LISA, we can test Einstein’s theory and see whether or not he was right."

As of November 2005, LIGO is up and running and could, in theory, detect gravitational waves from stellar-size black hole mergers any day. LISA, in the planning stages, could detect longer-wavelength gravitational radiation from supermassive black holes. The beauty of the NASA simulations is that they can be scaled to fit either scenario.