# [Users] Isotropic Initial Data Evolving Towards Anisotropy

Nick Olsen n.olsen.3.711 at gmail.com
Fri May 27 09:56:13 CDT 2022

Hello Erik

Forgive the late reply, it's been a busy few days. As I understand things
isotropic and spherically symmetric should be the same thing in this case,
with an isotropic metric taking the form -a(r)^2 dt^2+b(r)^2 ds^2, so the
fact that g_xx=/=g_yy and its value depends on direction is what has me
worried.

Nicholas Olsen

On Fri., May 13, 2022, 2:28 p.m. Erik Schnetter, <schnetter at gmail.com>
wrote:

> On Thu, May 12, 2022 at 3:28 AM Nick Olsen <n.olsen.3.711 at gmail.com>
> wrote:
>
>> Hello Everyone
>>
>> I am running into a problem where I evolve a Gaussian shell scalar field
>> alongside the BSSN equations using the Scalar/ScalarInit/ScalarBase thorns,
>> where the initial data is isotropic but evolves to an anisotropic solution.
>> More specifically, along the x axis I have g_yy=g_zz and along the z axis I
>> have g_xx=g_yy, with g_xx along the x axis equal to g_zz along the z axis,
>> despite having isotropic initial conditions. The point is illustrated by
>> the first image being the plot of g_xx and g_zz along their respective axes
>> at a later time, and the rest of the diagonal metric values being shown in
>> the second image. Additionally, T_ij shows a similar problem, where If so,
>> T_xx along the x axis and T_zz along the z axis are equal to eachother, but
>> not the rest of the diagonal entries of T_ij, which are all equal.
>>
>
> Nils
>
> What you describe sounds isotropic.
>
> I assume that by saying "isotropic" you mean "spherically symmetric", i.e.
> the solution only depends on the radius r and not on the angles \theta or
> \phi.
>
> If so, then scalars should be the same in every direction, vectors should
> point in the radial direction, and tensors will look a bit more
> complicated. but "g_xx in the x direction is the same as g_zz in the z
> direction" sounds correct: If you rotate this tensor from the x to the z
> axis, then you're essentially exchanging x and z directions.
>
> The tensor itself does not need to remain spherically symmetric. (From
> your description above it sounds as if you assumed this was the case.)
>
> -erik
>
>
>
>
>> [image: gxxx.PNG][image: gxxz.PNG]
>> I have attached the parameter file used to get these results, which is a
>> modified version of the test parameter file found in the Scalar thorn
>> bundle.
>>
>> Thanks,
>> Nicholas Olsen
>> _______________________________________________
>> Users mailing list
>> Users at einsteintoolkit.org
>> http://lists.einsteintoolkit.org/mailman/listinfo/users
>>
>
>
> --
> Erik Schnetter <schnetter at gmail.com>
> http://www.perimeterinstitute.ca/personal/eschnetter/
>
>
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