Trying to verigy Magnetohydrodynamics Formula

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sambit ratha

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Aug 23, 2021, 7:53:43 AM8/23/21
to xAct Tensor Computer Algebra

Hi

Consider the following two expressions that I want to verify the equality of:Screenshot 2021-08-23 at 3.24.28 PM.png
The first is from Blandford and Thorne's book on Modern Classical Physics. I have defined the relevant quantities, but get an index collision error when I try to canonicalize my final expression (1.9.44). The notebook is attached herewith.

Thanks.
ForceOperator.nb

Jose

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Aug 23, 2021, 8:00:41 AM8/23/21
to xAct Tensor Computer Algebra
Hi,

Your expression pertB contains

   epsilonmet[i, j, k] covD[-j][epsilonmet[k, l, m] xi[-l] B[-m] ]

which has a repeated k index. Change one to -k.

Note the message was ""Found indices with the same name k$6529"". That was an indication that the problem was with a k index.

Cheers,
Jose.

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