[Users] evolving a BH hole with Kerr-Schild ID in ET

[Zach Etienne]

Hi Roland,

> Additionally, I find it convenient to smooth all quantities near the
> > singularity, and to choose to advect both lapse and shift. I don't
> > know whether the latter is necessary in theory, but I am always using
> > it.
> Concerning the smoothing it seems that some smoothing was necessary to
> not crash the code (via the Exact epsilon parameter to transform r ->
> r+epsilon). An alternative may have been to use NoExcision to fill the
> interior of the AH with smooth data.


I generally suggest shifting the grid so that the closest gridpoint to the
origin is (dx/2, dy/2, dz/2), where dx,dy,dz are the resolutions on the
finest grid. I've used this trick many times to stabilize evolutions. Also
you may want to try the ShiftedKerrSchild thorn (in the ETK), which enables
a radial offset that shrinks the BH coordinate size but at the same time
kills off enormous constraint violations near r=0. Unlike the existing
KerrSchild thorn(s), this one uses the standard Kerr-Schild metric written
in spherical coordinates and does the basis xform.

-Zach

*     *     *
Zachariah Etienne
Assistant Professor of Mathematics
West Virginia University
*https://math.wvu.edu/~zetienne/ <https://math.wvu.edu/~zetienne/>*
https://blackholesathome.net


On Thu, Apr 25, 2019 at 12:30 PM Haas, Roland <rhaas at illinois.edu> wrote:

> Hello Erik,
>
> > This is almost possible. For puncture data, one typically evolves
> > lapse, shift, and a quantity B (the time derivative of the shift). For
> > Kerr-Schild data, one also needs to evolve A, the time derivative of
> > the lapse. Otherwise, Kerr-Schild data are not stationary. (One could
> > instead add an offset alpha_0 to the evolution equations for K, but
> > that is quite non-standard and not implemented in McLachlan.)
> Ok so it is possible.
>
> > Additionally, I find it convenient to smooth all quantities near the
> > singularity, and to choose to advect both lapse and shift. I don't
> > know whether the latter is necessary in theory, but I am always using
> > it.
> Concerning the smoothing it seems that some smoothing was necessary to
> not crash the code (via the Exact epsilon parameter to transform r ->
> r+epsilon). An alternative may have been to use NoExcision to fill the
> interior of the AH with smooth data.
>
> > I can send a sample parameter file if that helps.
> That would be great if you had something that you could send around
> easily.
>
> Yours,
> Roland
>
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