125 Reputation

15 years, 281 days

Scalar function in metric - Differential...

Maple 18

I am using Maple 18 on a Mac. I also uploaded the tetrad package.  I setup my metric but when I call Christoffel I get the following error.

I appreciate the help.

Writing symbols and equations...

Maple 18

I want to write an equation in the text portion of my document.  I do not need it evaluated. I just want to write formulas, like I do in LaTeX.

SubstitutionTensor command not seeing et...

The TensorSubstittuition is not finding all of the eta[~mu,~mu]*l[nu](X)=l[~mu](X) substitutions.

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The first term should change eta[~alpha,~beta]*l[alpha] -> l[~beta]. I made eta symmetric so the order should not matter. I notice that the command seems to work when the substitution is at the beginning of the term.  Do I need to use the new RepositionRepeatedIndicesAsIn command?

Substitution Tensor command has problem ...

Maple 18

I am having trouble with the SubstitutionTensor command.  It kicks out an error message for operand with different free indices, but the operands seems to be fine.  I checked all of the terms and they all seem fine. Thank you for your help.

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Arrangement of indices after Simplify...

Maple 18

After using Simplify the indices are are arranged in the tensor.  I am using the April 14th update from the Physics R&D page.

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We first define the Christoffel symbol in terms of the metric,   .

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Now we can substitute into the null condition for the Ricci tensor, .

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Do the first term

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Do same thing with the first term but use the Simplify command

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Simplify command does make the algebra easier, but the indices are not the same. Now, equation 16 should correspond to equation 14, but there is no combination of alphas that is consistent.  The variables alpha1 and alpha5 must be rho. One term is always wrong when I try to change the other indices.

alpha2 and alpha3 must be either mu or nu based on the first term.  But alpha6 should also be either mu or nu based on the last term, however that will make alpha2 and alpha3 either (nu and rho) or (mu and rho).  Neither combination makes all of the terms consistent with (14).  Very frustrating.

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