Hello Ian,
While working on a hydro code for CarpetX the people involved (in cc via the mailing list) ran into the issue of how to handle the lapse the show up in the flux of the fluid equations.
E.g. in GRHydro (nee Whisky) one uses a numerical flux of (say for D) in https://www.einsteintoolkit.org/thornguide/EinsteinEvolve/GRHydro/documentat...
as F^i_D = D (\alpha v^i - \beta^i) yet the flux expressions used in the Riemann problem are computed as:
\tilde F^i_D = D (v^i - \beta^i/\alpha)
ie a factor of the lapse has been divided out.
It gets put back when the fluxes are combined to compute a right hand side by using:
RHS = \alpha_{i-1/2} F^j(x_{i-1/2}) - \alpha_{i+1/2} F^j(x_{i+1/2})
None of the CarpetX developers (with the possible exception of Erik, but his expertise is in a different area and in any case he does not remember) were involved in the original Whisky code.
So: do you remember if there was a specific reason why the lapse was divided out in the expressions used in the Riemann problem?
Yours, Roland