ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 11 Nov 2018 10:04:03 -0600Killing vectorshttp://ask.sagemath.org/question/44222/killing-vectors/Hi All,
Given a space-time metric, is there a way to calculate its Killing vectors?
Thanks,
Daniel Volinski
Thu, 08 Nov 2018 05:49:32 -0600http://ask.sagemath.org/question/44222/killing-vectors/Answer by tmonteil for <p>Hi All,</p>
<p>Given a space-time metric, is there a way to calculate its Killing vectors?</p>
<p>Thanks,</p>
<p>Daniel Volinski</p>
http://ask.sagemath.org/question/44222/killing-vectors/?answer=44223#post-id-44223Sage Manifolds should do that, see for example :
- https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Kerr.ipynb
- https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Kerr_Newman.ipynb
- https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Simon-Mars_Curzon-Chazy.ipynb
Though those examples seem to check that some vector fields are Killing vector, there should be way to ask Sage to solve the differential equation.Thu, 08 Nov 2018 06:22:33 -0600http://ask.sagemath.org/question/44222/killing-vectors/?answer=44223#post-id-44223Comment by tmonteil for <p>Sage Manifolds should do that, see for example : </p>
<ul>
<li><a href="https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Kerr.ipynb">https://nbviewer.jupyter.org/github/s...</a></li>
<li><a href="https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Kerr_Newman.ipynb">https://nbviewer.jupyter.org/github/s...</a></li>
<li><a href="https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Simon-Mars_Curzon-Chazy.ipynb">https://nbviewer.jupyter.org/github/s...</a></li>
</ul>
<p>Though those examples seem to check that some vector fields are Killing vector, there should be way to ask Sage to solve the differential equation.</p>
http://ask.sagemath.org/question/44222/killing-vectors/?comment=44241#post-id-44241Yup !Sun, 11 Nov 2018 10:04:03 -0600http://ask.sagemath.org/question/44222/killing-vectors/?comment=44241#post-id-44241Comment by eric_g for <p>Sage Manifolds should do that, see for example : </p>
<ul>
<li><a href="https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Kerr.ipynb">https://nbviewer.jupyter.org/github/s...</a></li>
<li><a href="https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Kerr_Newman.ipynb">https://nbviewer.jupyter.org/github/s...</a></li>
<li><a href="https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Simon-Mars_Curzon-Chazy.ipynb">https://nbviewer.jupyter.org/github/s...</a></li>
</ul>
<p>Though those examples seem to check that some vector fields are Killing vector, there should be way to ask Sage to solve the differential equation.</p>
http://ask.sagemath.org/question/44222/killing-vectors/?comment=44226#post-id-44226Not to my knowledge. It would be a nice addition to Sage to express the Killing equation as a system of linear 1st order PDEs and attempt to solve those.Thu, 08 Nov 2018 10:40:41 -0600http://ask.sagemath.org/question/44222/killing-vectors/?comment=44226#post-id-44226Comment by danielvolinski for <p>Sage Manifolds should do that, see for example : </p>
<ul>
<li><a href="https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Kerr.ipynb">https://nbviewer.jupyter.org/github/s...</a></li>
<li><a href="https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Kerr_Newman.ipynb">https://nbviewer.jupyter.org/github/s...</a></li>
<li><a href="https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.3/SM_Simon-Mars_Curzon-Chazy.ipynb">https://nbviewer.jupyter.org/github/s...</a></li>
</ul>
<p>Though those examples seem to check that some vector fields are Killing vector, there should be way to ask Sage to solve the differential equation.</p>
http://ask.sagemath.org/question/44222/killing-vectors/?comment=44224#post-id-44224Thank you for those excellent examples but, as you mentioned above, I precisely need "the way to ask Sage to solve the differential equation". May be somebody already solve this problem...
Thanks,
DanielThu, 08 Nov 2018 09:58:45 -0600http://ask.sagemath.org/question/44222/killing-vectors/?comment=44224#post-id-44224