Some Questions & Issues Posed by Ashtekar
- 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?
- 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?
- 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.