questions on xCoba. Do not get Bianchi identity for a simple metric.

[jjlvillarejo]

Dear all,

I followed the example of the Kerr-Newman metric for xCoba, just
changed the metric for simple ones as diag(1, -a(t)^2, -a(t)^2, -a(t)
^2 ) or diag (t, t^2, xy, xy) (my coordinates are t,x,y,z), and then
I do not get the Bianchi identity right. This identity is independent
of the metric used, isn't it?

Changes with respect to 'xActKerrNewmanExamples.nb':

DefChart[B, M, {0, 1, 2, 3}, {t[], x[], y[], z[]}]

MatrixForm[KerrMetric = {
{-t[]^2, 0, 0, 0},
{0, t[]^2, 0, 0},
{0, 0, (x[] y[])^2, 0},
{0, 0, 0, (x[] y[])^2}
}]

(I used last version of xAct.)


Also, I would like to use scalars on this spacetime that do not depend
on the spatial coordinates x,y,z, but only on t. How could I implement
this?
Regards,

Juan

[jjlvillarejo]

Sorry, it was

diag(-t^2, t^2, (xy)^2, (xy)^2)


On Oct 29, 6:34 pm, jjlvillarejo <juan.jose.lopez.villar...@gmail.com>
wrote:

[JMM]

Thanks Juanjo!

Of course, the Bianchi identity must be true for all metrics!

I've had a look and found that I forgot to add the /2 in Einstein =
Ricci - RicciScalar/2 in the new, faster, code for component
computations. It was unlucky that the tests were done with Kerr-
Newman, a metric with zero Ricci scalar...

So, everybody using the last version of xAct (0.9.9) go to xCoba.m and
in the line 2361, where it says

RicciPointer[i,j]-RicciScalarPointer[]MetricPointer[i,j]

you add the /2, so that it reads

RicciPointer[i,j]-RicciScalarPointer[]MetricPointer[i,j]/2

Thanks again Juanjo. That was a bigbug!

Cheers,
Jose Maria.


On Oct 29, 6:38 pm, jjlvillarejo <juan.jose.lopez.villar...@gmail.com>
wrote:

[JMM]

> Also, I would like to use scalars on this spacetime that do not depend
> on the spatial coordinates x,y,z, but only on t. How could I implement
> this?

Hi again,

Concerning this, you have to use scalar-functions. For example,
declare a function f with

DefScalarFunction[f]

and then work with f[ t[] ], or f[ t[], x[] ], etc. Let me use the
opportunity to explain the difference between scalar fields and scalar-
functions in xTensor. The scalar fields are maps from the manifold to
R (the reals), but the scalar-functions are maps from R^n to R, where
n is the number of arguments. The combined object f[ t[], x[] ] is a
scalar field as well. You can declare a scalar field F with DefTensor
[ F[], M ], and then replace F[] by f[ t[], x[] ]. In that sense f is
the coordinated form of F. This is an important but subtle difference.
Somebody called this once "The first fundamental confusion of
calculus"...

Cheers,
Jose.

[magma]

I have not been able to find this line in the latest xCoba.m (24 Nov
2009).
Has this bug already been fixed in the 24 Nov 2009 version?

[JMM]

Yes. This was one main reason to rerelease 0.9.9. You can see the
changes from version to version by checking the History files of the
packages. For example in this case it would be
http://metric.iem.csic.es/Martin-Garcia/xAct/xCoba/xCoba.History .
These files are part of the xAct_version.tar.gz bundle.

Cheers,
Jose.

[magma]

Indeed! I realized this a few minutes after posting the message.
I am still very new to the wonderful xAct package suite and had not
explored the website thoroughly.

I would draw your attention to the main xTensor page at:
http://metric.iem.csic.es/Martin-Garcia/xAct/xTensor/index.html

and also to the xCoba page at:
http://metric.iem.csic.es/Martin-Garcia/xAct/xCoba/index.html

Both still report the 9 Sep 2009 as the latest version.

I became aware of the existence of the 24 Nov 2009 version only by
reading the 11 Dec 2009 post.

I would also suggest that even minor patches should be advertised on
this forum.

[JMM]

On Dec 12, 7:38 pm, magma <mader...@gmail.com> wrote:

> I would draw your attention to the main xTensor page at:http://metric.iem.csic.es/Martin-Garcia/xAct/xTensor/index.html
>
> and also to the xCoba page at:http://metric.iem.csic.es/Martin-Garcia/xAct/xCoba/index.html
>
> Both still report the 9 Sep 2009 as the latest version.

Thanks. I update these numbers manually, and hence forget some of
them... Fixed now.

> I would also suggest that even minor patches should be advertised on
> this forum.

Sounds reasonable.

Thanks again,
Jose.