Einstein's equations with asymptotically stable constraint propagation

We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables o f the modified system are essentially first integrals of the original const raints. The extended system of equations reproduces the usual dynamics on t he constraint surface of general relativity, and therefore naturally includ es the solutions to Einstein gravity. The main feature of this extended sys tem is that, at least for a linearized version of it, the constraint surfac e is an attractor of the time evolution. This feature suggests that this sy stem may be a useful alternative to Einstein's equations when obtaining num erical solutions to full, nonlinear gravity. (C) 1999 American Institute of Physics. [S0022-2488(99)03002-9].