[Developers] Storing gauge time derivatives in ADMBase

[Erik Schnetter]

The ADMBase variables store currently the 3-metric, lapse, shift, and  
extrinsic curvature.  They do not store the time derivatives of lapse  
and shift, which makes it impossible to calculate the time derivative  
of the 4-metric from the ADMBase variables.  This is a shortcoming,  
since almost all current evolution systems require these, including  
common BSSN gauge conditions and harmonic evolution schemes.  (In many  
cases, initial data assume that these additional time derivatives are  
zero to get around this issue.)

The enclosed patch adds grid functions for dtlapse and dtbetax,  
dtbetay, and dtbetaz.  It also adds a few state variables so that  
codes can determine whether these variables have storage; storage is  
off by default for backwards compatibility.  This is similar to the  
shift vector, which also has no storage by default.

-erik

-- 
Erik Schnetter <schnetter at cct.lsu.edu>   http://www.cct.lsu.edu/~eschnett/

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