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To the Third Dimension and Back

Numerical Relativity Timeline

Three-dimensional codes will finally allow physicists to study black holes as they might actually exist: non-symmetric and spinning rapidly. Not surprisingly, three-dimensional models are much more complex than their 1D and 2D counterparts; adding the extra dimension leads to equations with thousands of terms each. Special software such as Mathematica, Macsyma, or other computer algebra programs must be used just to derive and symbolically manipulate the terms, then code them into a computer language like Fortran.

Computional Infrastructure

Running the resulting three-dimensional codes demands the memory and speed of massively parallel computers.

A few years ago it would have taken scientists using the CRAY Y-MP about 100,000 hours to perform an accurate 3D simulation of two spiralling black holes. Today, using algorithms optimized for parallel machines, this timeframe has been cut by about 100 times, to 1000 hours on a Thinking Machines' Connection Machine 5 or CM- 5. However, due to the immense computer memory requirements for such calculations, the full solution of this important problem cannot yet be computed on either machine. Although NCSA's CM-5 supercomputer possesses 64 times the memory of its Cray Y-MP, the calculation demands another 100-fold increase in memory.

To this end, NCSA researchers are experimenting with different scalable, microprocessor-based arrays of computers such as the Silicon Graphics Power Challenge and the Convex Exemplar. At other Federally-funded supercomputer centers there are machines such as Cornell's new IBM SP-2 or Pittsburgh's Cray T3D and C90 that in various combinations could enable researchers to reach nearer to this goal.

At present, though, researchers are restricted to tackling simpler problems, such as computing spacetimes in 3D for a single black hole or two holes of equal mass that are colliding head-on, but not orbiting each other. Fully calculating the 3D solution for spiralling black holes awaits the arrival of teraflop machines with a terabyte of memory.

But the scale and complexity of such calculations demand much more than powerful computers to solve them. Meeting this challenge requires that geographically dispersed numerical relativists, astrophysicists, and computer scientists forge an alliance -- a Grand Challenge Alliance.

First, Back to Basics

Although members of the Alliance have developed three-dimensional codes, the codes are so complex that first they are being applied to the well-tested one- and two-dimensional systems. One of the first tests has been to apply the 3D code to the data that describes the spherical Schwarzschild black hole.

The solution to the problem is known from the 1D studies: will the scientists get the same answer using a 3D code? They should (and they do!) but, as of the summer of 1995, the scientists are finding that they do not yet have enough computing power --even on a massively parallel machine like the CM-5 -- to get an accurate 1D model for long simulations using 3D code. However, early results look promising, according to very recent data. New techniques that will allow much longer calculations are progressing well.

Now the Alliance is beginning to test the 3D code on 2D black hole models. Already preliminary movies have been generated and are now being refined. Soon the scientists hope to begin the best test yet of the 3-D code: applying the code to 2D colliding black holes.

The scientists of the Alliance are also taking their 3D codes one step further. They are using their 3D codes to model the propagation of gravitational waves through space -- a true three-dimensional problem without the complications of a black hole and quantities approaching infinity. Early results are very encouraging.

Movie of Gravitational Waves in 3D

Such test simulations may yield some very useful and interesting results. Theory predicts that a very strong gravitational wave could act as a source of gravity for itself, turning inward and forming its own black hole. Although a phenomenon of mainly theoretical interest -- it is unlikely that any gravitational wave could be so strong -- this exotic simulation could yield valuable information about the behavior of gravitational waves, further exploring Einstein's theory as applied to highly distorted spacetimes. Not only will this knowledge prove useful when the first gravitational wave detectors go "online," it will also help guide the construction of the next generation of codes to probe Einstein's theory of spacetime itself.

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

NCSA. Last modified 11/9/95.