Markus Hanke 487 Posted August 21, 2020 Share Posted August 21, 2020 I am currently working on a GR related project, and I wonder if there is anyone here who has access to a MAPLE installation? I need help to save me lots of work with the following: suppose we have a GR spacetime endowed with the usual Levi-Civita connection and the metric \[ds^{2} =-\left( 1-\frac{2M( u)}{r}\right) du^{2} -2dudr+r^{2}\left( d\theta ^{2} +sin^{2} \theta d\phi ^{2}\right)\] wherein M(u) is an unspecified everywhere differentiable function. My task is now to find all non-vanishing Christoffel symbols (2nd kind) for this metric, in terms of the mass function M(u) and its derivatives. I could of course do this by hand with pen-and-paper, but this is tedious, time consuming, and error prone; MAPLE has a differential geometry module that can automate this task. Is there anyone here who might be able to run this through MAPLE for me, and post the Christoffel symbols? This would save me lots of work and time To give a wider context, I need the Christoffel symbols so that I can write down the geodesic equations, and solve them for a purely radial free fall from rest at infinity. The above metric describes the exterior of a Vaidya black hole; I know already that the in-fall time from infinity to horizon is finite and well defined (unlike in Schwarzschild spacetime), but I need to find an explicit expression for that in-fall time in terms of the mass function M(u). Thank you in advance Link to post Share on other sites

Strange 4272 Posted August 21, 2020 Share Posted August 21, 2020 Have you looked to see if anything equivalent is available for Octave? (I am not very familiar with any of these packages, so I have no idea) Also, there is a 15 day trial version of Maple (but maybe you have used that up already 🙂) Link to post Share on other sites

joigus 369 Posted August 21, 2020 Share Posted August 21, 2020 I don't know about MAPLE, but I think there is a Mathematica package to calculate Christoffel symbols. I've found this discussion which may be useful for the Mathematica option: https://mathematica.stackexchange.com/questions/8895/how-to-calculate-scalar-curvature-ricci-tensor-and-christoffel-symbols-in-mathem Link to post Share on other sites

Markus Hanke 487 Posted August 21, 2020 Author Share Posted August 21, 2020 1 hour ago, Strange said: Have you looked to see if anything equivalent is available for Octave? (I am not very familiar with any of these packages, so I have no idea) Also, there is a 15 day trial version of Maple (but maybe you have used that up already 🙂) I have never heard of Octave, so not sure about this. As for MAPLE, my main work computer is an iPad Pro (I live off-grid on a 12V solar system), so this is not an option. 31 minutes ago, joigus said: I don't know about MAPLE, but I think there is a Mathematica package to calculate Christoffel symbols. I've found this discussion which may be useful for the Mathematica option: https://mathematica.stackexchange.com/questions/8895/how-to-calculate-scalar-curvature-ricci-tensor-and-christoffel-symbols-in-mathem I’m afraid I don’t have access to Mathematica either. Link to post Share on other sites

joigus 369 Posted August 21, 2020 Share Posted August 21, 2020 3 minutes ago, Markus Hanke said: [...] I’m afraid I don’t have access to Mathematica either. You've got a free web portal: https://www.wolframalpha.com/ And if you need more computation power and time, server dedication, (plus access to some packages, etc.), you can download an app for about not much more than 2€, if I remember correctly. I think it's money well spent. Link to post Share on other sites

studiot 2145 Posted August 21, 2020 Share Posted August 21, 2020 (edited) I have an older version MathCad. This is not compatible with Mathematica / Maple however (or Latex/) I haven't looked but are there any ready made packages available from Wolfram Alpha, that wouldn't suprise me at all. #Geogebra might be able to do it, and its free https://www.geogebra.org/?lang=en-GB Another free one is Maxima. This one boasts tensor calculations http://maxima.sourceforge.net/ What exactly do you want to run? Is it numerical or symbolic ? https://en.wikipedia.org/wiki/List_of_numerical-analysis_software Edited August 21, 2020 by studiot Link to post Share on other sites

joigus 369 Posted August 21, 2020 Share Posted August 21, 2020 Also, maybe Cadabra, for symbolic calculations, especially suited for field theory: https://cadabra.science/ I haven't tested it, to tell you the truth. Link to post Share on other sites

Markus Hanke 487 Posted August 21, 2020 Author Share Posted August 21, 2020 38 minutes ago, studiot said: What exactly do you want to run? I don’t have anything to run as such. I used to have a MAPLE installation, and in MAPLE there was a package where you just inputted the components of the metric tensor (in symbolic notation), and it would symbolically calculate the Christoffel symbols (as well as Ricci, Riemann, Einstein and Weyl tensors). I was just hoping that someone here might have access to MAPLE and thus a way to do this for me, since finding all the non-vanishing Christoffel symbols is tedious and quite frankly a pain in the backside. I have never used any other CAM software, so I’m not sure if this is possible with other applications also. It’s probably a long shot though Link to post Share on other sites

Strange 4272 Posted August 21, 2020 Share Posted August 21, 2020 1 hour ago, Markus Hanke said: I have never heard of Octave, so not sure about this. It is an open-source equivalent to Mathematica (and, presumably, similar to Maple): https://www.gnu.org/software/octave/ (I have only used it for some basic linear algebra when studying ML) There is an online version: https://octave-online.net Otherwise, I would think Wolfram Alpha may be the best bet Link to post Share on other sites

Markus Hanke 487 Posted August 21, 2020 Author Share Posted August 21, 2020 Ok, thanks! This can’t do what I need it to do, as far as I can see...but that’s ok, I’ll just have to sit down and do it by hand. It’ll take more time, but I’ll get there (eventually) Link to post Share on other sites

studiot 2145 Posted August 21, 2020 Share Posted August 21, 2020 This definitive paper suggests there is an online #Wolfram package for this. I will try to find it later. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6105178/ 1 Link to post Share on other sites

Samir Khan 0 Posted August 25, 2020 Share Posted August 25, 2020 (edited) @Markus Hanke Could you post the request on MaplePrimes.com? They're a helpful bunch. Or let me know and I'll get you a Maple trial (I work for Maplesoft). Edited August 25, 2020 by Samir Khan Link to post Share on other sites

Markus Hanke 487 Posted August 26, 2020 Author Share Posted August 26, 2020 20 hours ago, Samir Khan said: @Markus Hanke Could you post the request on MaplePrimes.com? They're a helpful bunch. Or let me know and I'll get you a Maple trial (I work for Maplesoft). Thanks, I might post it there, didn’t even think of that. I do not have access to a desktop computer (long story), so I’m afraid the trial won’t work for me. Link to post Share on other sites

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