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Beyond the Spherical Cow

Numerical Relativity Timeline

Once they settle down, black holes are thought to be very simple, spherical objects which cannot emit substantial gravity waves. However, when black holes form from gravitational collapse or are disturbed in some way, for example by infalling matter, their geometry becomes much more complex, at least until they settle back. During this period, the disruption of the surrounding space causes gravitational waves, much like a bell rings after being struck.

Clearly, if scientists are to detect and pinpoint black holes or other objects via their gravitation radiation, they must be able to solve the Einstein equations for spacetimes beyond those of perfect spheres!

Codes to Run By

Two-dimensional, dynamic (e.g., wobbling, expanding, contracting) axisymmetric spacetimes (think of a football: not round, but symmetric about an axis) can emit gravitational waves. The equations used to describe the axisymmetric models are much more complex than those used to describe the Schwarzschild black hole, requiring more elaborate algorithms, thousands of lines of code and much greater computer power to crunch the numbers. The payoff? Much richer physics and a better understanding of the behavior of black holes, as they might really exist in the universe.

Resonating and Ringing

One of the first axisymmetric models, developed in the late 1980's, showed the changes that occur to a black hole disturbed and distorted by a gravitational wave. The black hole begins to oscillate; some of the gravitational waves are swallowed, while others waves escape. The black hole rather quickly sheds its distortions by emitting gravitational waves. The movies in this exhibit depict the vibrations resulting from a weak, then strong gravitational disturbance.

Movies of Distorted Black Holes

Colliding Head-On

Soon afterwards scientists modeled two non-rotating black holes colliding head-on due to their gravitational attraction. As they collide, their event horizons overlap, then merge as they form a single, larger black hole. Animations of the gravitational waves emitted reveal that they are very similar to those given off by a single black hole hit by a very strong gravitational wave.

In a related simulation by NCSA's Relativity Group, the escape of light particles (photon torpedoes) was visualized close to a horizon formed from the merger of two black holes. The resulting movie shows that light can escape from just outside the new event horizon, but not from within.

Movie of Colliding Black Holes

Movie of "Photon Torpedoes"

The colliding black hole model cannot yield an accurate picture of a "real" collision, because it is only axisymmetric, but it paves the way for a more generalized or realistic, 3D model: two black holes spinning, revolving around each other, and finally colliding. These simulations have also spurred scientists in the the relativity research community to grapple with the physics of black hole collisions and come up with new analytic techniques to study them.

Ed Seidel, NCSA/Univ. of Illinois, on-camera
Movie/Sound Byte
QuickTime Movie (1.7 MB); Sound File (1.0 MB); Text

Rotating for Real

Finally, the relativists incorporated rotation in the model, a major step that adds a great deal of physics. The model of a 2D rotating black hole prepared the scientists for the complexities of adding a third dimension to their calculations.

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Copyright 1995, The Board of Trustees of the University of Illinois

NCSA. Last modified 11/9/95.