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Brady, Creighton and Thorne have argued that, in numerical relativitysimulations of the inspiral of binary black holes, if one uses lapse and shiftfunctions satisfying the ``minimal strain equations'' (MSE), then thecoordinates might be kept co-rotating, the metric components would then evolveon the very slow inspiral timescale, and the computational demands would thusbe far smaller than for more conventional slicing choices. In this paper, wederive simple, testable criteria for the MSE to be strongly elliptic, therebyguaranteeing the existence and uniqueness of the solution to the Dirichletboundary value problem. We show that these criteria are satisfied in a test-bedmetric for inspiraling binaries, and we argue that they should be satisfiedquite generally for inspiraling binaries. If the local existence and uniquenessthat we have proved holds globally, then, for appropriate boundary values, thesolution of the MSE exhibited by Brady et. al. (which tracks the inspiral andkeeps the metric evolving slowly) will be the unique solution and thus shouldbe reproduced by (sufficiently accurate and stable) numerical integrations.Comment: 6 pages; RevTeX; submitted to Phys. Rev. D15. Technical issue of the  uniqueness of the solution to the Dirichlet problem clarified. New subsection  on the nature of the boundary dat

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Integrability of the minimal strain equations for the lapse and shift in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>numerical relativity

Integrability of the minimal strain equations for the lapse and shift in3+1numerical relativity