[Developers] CactusEinstein/2052: Patch: Add time derivatives of lapse and shift as new variables

schnetter at cct.lsu.edu schnetter at cct.lsu.edu
Thu Sep 7 09:29:59 CDT 2006


>Number:         2052
>Notify-List:    developers at cactuscode.org
>Category:       CactusEinstein
>Synopsis:       Patch: Add time derivatives of lapse and shift as new variables
>Confidential:   no
>Severity:       serious
>Priority:       medium
>Responsible:    rideout
>State:          open
>Class:          feature-request
>Submitter-Id:   user
>Arrival-Date:   Thu Sep 07 09:29:59 -0500 2006
>Originator:     Erik Schnetter
>Release:        Cactus 4.0.b16
>Organization:
>Environment:
>Description:
I suggest to add the time derivatives of lapse and shift as additional variables to ADMBase.  Together with the extrinsic curvature, this allows constructing the time derivative of the four-metric.  This "completes" the set of variables; since the Einstein equations are second order in time, initial data for them have to set both the four-metric and its time derivative.

This is necessary to provide complete initial data to some formulations of Einstein's equations which are not based on lapse and shift.  It also allows using exact solutions with such formulations.

The new variables have no storage by default.  Their storage is handled in the same way as for the shift, i.e., via parameters and a run time state variable.

Later, other thorns (such as AEIThorns/Exact) would be modified to set these variables as well when they have storage.
>How-To-Repeat:
>Fix:
Unknown
>Unformatted:
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