# [Users] Isotropic Initial Data Evolving Towards Anisotropy

Erik Schnetter schnetter at gmail.com
Fri May 13 13:28:24 CDT 2022

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
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>

--
Erik Schnetter <schnetter at gmail.com>
http://www.perimeterinstitute.ca/personal/eschnetter/
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