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Many alternative formulations of Einstein's evolution have lately beenexamined, in an effort to discover one which yields slow growth ofconstraint-violating errors. In this paper, rather than directly search forwell-behaved formulations, we instead develop analytic tools to discover whichformulations are particularly ill-behaved. Specifically, we examine the growthof approximate (geometric-optics) solutions, studied only in the future domainof dependence of the initial data slice (e.g. we study transients). Byevaluating the amplification of transients a given formulation will produce, wemay therefore eliminate from consideration the most pathological formulations(e.g. those with numerically-unacceptable amplification). This technique hasthe potential to provide surprisingly tight constraints on the set offormulations one can safely apply. To illustrate the application of thesetechniques to practical examples, we apply our technique to the 2-parameterfamily of evolution equations proposed by Kidder, Scheel, and Teukolsky,focusing in particular on flat space (in Rindler coordinates) and Schwarzchild(in Painleve-Gullstrand coordinates).Comment: Submitted to Phys. Rev.

Geometrical optics analysis of the short-time stability properties of the Einstein evolution equations