[Users] About the thorn Einstein exact

[Nisa Amir]

Yes, the mathematica package is given but it accepts the metric only in
cartesian coordinates. I want to add the spacetime non kerr which is in
polar coordinates to the mathematica package in Einstein Exact thorn. What
transformations should I made?

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On Mon, Nov 6, 2017 at 9:11 PM, Ian Hinder <ian.hinder at aei.mpg.de> wrote:

>
> On 5 Nov 2017, at 09:28, Nisa Amir <nisaamir at math.qau.edu.pk> wrote:
>
> > Actually, when in the einsteinexact thorn there is a mathematica package
> named EinsteinExact. The documentation said that if you want to add some
> new space time add the space time in that mathematica package. I want to
> add non kerr which is in polar coordinates to that package, so that it
> generates a new thorn but I dont know how to do that.
> > Kindly guide me.
>
> Hi,
>
> Yes, you can add a new spacetime to the Metrics package (in
> Cactus/arrangements/EinsteinExact/m/Metrics/metrics). See the examples in
> there.  For example, Schwarzschild.m:
>
> (* ::Package:: *)
>
> {
>   "Name" -> "Schwarzschild",
>   "Description" -> "Schwarzschild spacetime",
>   "Dimensions" -> 4,
>   "Coordinates" -> {t, r, \[Theta], \[Phi]},
>   "Parameters" -> {M},
>   "Metric" -> {{-1 + 2 M / r, 0, 0, 0},
>                {0, 1/(1 - 2 M / r), 0, 0},
>                {0, 0, r^2, 0},
>                {0, 0, 0, r^2 Sin[\[Theta]]^2}},
>   "SignDet" -> -1
> }
>
> The EinsteinExact package then uses this information to generate an exact
> solution thorn, which can be used for initial data in a numerical
> relativity evolution.   However, it only supports metrics which are
> explicitly given in Cartesian coordinates, so for example, the
> Schwarzschild example won't work with it (the Metrics package is generic,
> and is used also in other contexts, outside EinsteinExact).
>
> There is a check in arrangements/EinsteinExact/m/EinsteinExact.m that the
> metric is in Cartesian coordinates.  I suspect that the only reason for
> this check is that it wouldn't know what Cactus gridfunctions to use for
> anything else.
>
> Since you want to do the evolution in polar coordinates, I assume that you
> are going to have some mapping between x, y and z, and r, th and ph?  I
> must admit I have never tried to do something like this.
>
> There are people on this list who have done evolutions in polar
> coordinates; maybe one of them could give some advice about whether what
> you are trying to do is feasible?  Maybe you could give more details about
> what you are trying to do?
>
> PS: *please* include users at einsteintoolkit.org in the CC when you reply.
> If you reply just to me, then nobody else benefits from the discussion, and
> nobody else has the opportunity to help you.
>
> --
> Ian Hinder
> http://members.aei.mpg.de/ianhin
>
>
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