Some Questions & Issues Posed by Ashtekar

  1. There seems to be a tension between what we read in the mathematical literature on symmetric, first order hyperbolic systems (SFOHS) and what we are told happens in actual simulations. A motivation for these systems is often that they will ensure stability. But actual simulations based on SFHS do not bear this out. What is happening here?
  2. Do any of the SFOHS formulations take in to account the boundary conditions? Shouldn't they? Can we have a well-defined notion without worrying about boundary conditions? What is the relation between Friedrich-Nagy analysis and the available SFOHS?
  3. Linearized vs Non-linear: At one stage, the Texas group found instabilities already in the linear analysis. The claim was that these arise because of gauge modes. What is the current status of these? (Incidentally, even analyticaly These still persist after fixing lapse and shift.) The Potsdam group seems to do non-linear evolution without encountering these. How does this come about? These seems to be some tension between the two results.