The exponential growth of constraint violations is one of the most urgent problems facing the numerical relativity community today. These constraint violations cause most numerical solutions of the Einstein evolution equations quickly to become unphysical. One method of controlling this problem is to project the solutions back onto the constraint submanifold whenever the constraint violations become too large. Since there is not a unique projection, however, there is no guarantee that the resulting numerical method will be convergent.
Recent work by the Caltech numerical relativity group on defining optimal constraint projections will be discussed.
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