Not every 3-metric is conformally flat



Greetings, and thanks for your reply!  So if I understand you,

1) you agree that the response "this spacetime is conformally flat"
   needs revision
2) there is a genuine issue with tsetup/xmaxima/gcl-cmucl-sbcl.

Should these be entered into maxima's bug system?  Specifically with
regardsa to 2), is there any understanding why this is lisp
implementation dependent?  I take it this is not a readline issue?

I agree with your other comments regarding the proper syntax for
computing the weyl tensor.

Many thanks again,

Valery Pipin <pip@iszf.irk.ru> writes:

> Hello,
> 
> On Monday 26 May 2003 00:00, Camm Maguire wrote:
> CM>forwarded 191671 maxima@www.ma.utexas.edu
> CM>thanks
> CM>
> CM>
> CM>Greetings!  This bug has been filed by a Debian maxima user and looks
> CM>to be an issue with maxima proper.  I'm away from my email until 6/1,
> CM>and cannot receive sourceforge mail as my ISP blocks it as spam.  I
> CM>therefore cannot usefully register the bug on the website.  Please
> CM>excuse therefore the submission to this list instead.
> CM>
> CM>
> CM>Package: maxima
> CM>Version: 5.9.0-10
> CM>
> CM>The output of computing the Weyl tensor on an arbitrary 3 metric says
> CM>that the spacetime is conformally flat.
> If in short, it seems to me this is not a bug. The maxima's reply could be 
> made more accurate, however.
> 
> CM>(C2) g=tsetup();
> Sorry, I don't understand this. Function tsetup() make so many things at once 
> so we can not use the equation assignment
> Just as advice, we must compute the components of the Christoffel symbols and 
> components of Ricci tensor before to compute the Weyl tensor.
> 
> CM>(C3) weyl(g);
> The rigth syntax here weyl(dis) .if  dis:true then non zero component of the 
> Weyl tensor will be shown 
> CM>
> CM>this spacetime is conformally flat
> This is a standard reply for the case  and if the components of the Ricci 
> tensor are zero.
> The message is likely not correct in the general case, however. Rigth below 
> the "rigth" sequence to compute the Weyl tensor. Another example can be found 
> in the "swartz.dem"
> 1) tsetup(), Note the coordinates names (case sensitivity!!) have to be in 
> correspondence with the metric defined
> 2) christof(all);
> 3) lriccicom(all);weyl(true);
> CM>On a related note, xmaxima does not respond to the tsetup(); command, it
> CM>never responds with the line
> This behaviour with tsetup() is typical for xmaxima on gcl & cmucl as well. 
> Everything is ok for clisp. Actually. for the tensor packages in maxima the 
> clisp is the best choice. The issue with tsetup() could be overcame however.
> What's tsetup() designed for? It is designed to define the metric.
> So instead to use the function tsetup(). You could 1)define coordinates 
> through omega:[x,y,z], 2)define the metric via lg :   
> matrix([x,0,0],[0,y,0],[0,0,z]), 3)compute inverse metric ug:invert(lg). 
> These steps are usually done with tsetup().
> rgds,
> v
> 
> 
> 
> 
> 

-- 
Camm Maguire			     			camm@enhanced.com
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"The earth is but one country, and mankind its citizens."  --  Baha'u'llah