xPert GaugeChange

[Sam Finn]

I'm getting some contradictory results in my use of GaugeChange (part of the xPert package). A MWE, attached, shows two very straightforward and direct computations of a gauge change a the perturbed metric yield different results, one manifestly incorrect (or so it appears). 

Can some xPert expert comment? Am I making an ask here that is subtlety (at least to me) illegitimate? 

Thanks!

[Leo Stein]

Hi Sam,

When you created your automatic replacement rule with IndexSet, you used the result of performing the gauge change on the inverse (contravariant) metric. IndexSet made a definition that takes any index character in both slots — up or down. Putting downstairs indices into your gNew means lowering the indices on the result of gauge-changing the inverse metric, rather than performing the gauge change on the (covariant) metric.

Best

Leo

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[Sam Finn]

Aha! Stubbed my toe on how the h participate in the inverse metric, as opposed to as “stand alone” tensor fields. 

Thanks much, Leo. 

—

Sam Finn
lsf...@gmail.com