Anyone here with access to MAPLE?

[Markus Hanke]

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  

[Strange]

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 🙂)

[joigus]

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

[Markus Hanke]

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.

[joigus]

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.

[studiot]

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

[joigus]

Also, maybe Cadabra, for symbolic calculations, especially suited for field theory:

https://cadabra.science/

I haven't tested it, to tell you the truth.

[Markus Hanke]

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 

[Strange]

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

[Markus Hanke]

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)   

[studiot]

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/

[Samir Khan]

@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

[Markus Hanke]

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.