xPert: Series Expansion of a Function of the Metric

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Andrey

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Nov 15, 2024, 9:35:33 AMNov 15
to xAct Tensor Computer Algebra
Hello!

I am new to xPert as well as xAct, and I have a simple question:

DefManifold[M, 4, {a, b, c, d, e, f, i, j, k, l, m, n}]
DefMetric[-1, MT[-a, -b], CD, PrintAs -> "g"]
DefMetricPerturbation[MT, h, \[Epsilon]]

I would like to define a function of h, such as exp(h), with the same lower indices as h has. How should I code this? Specifically, I want to perform a series expansion as follows (in LaTeX notation):

(\exp(h))_{ab} = \delta_{ab} + h_{ab} + \frac{1}{2} h_{ac} h{cb} + \ldots

Additionally, I have a small question: how can I check if h is an antisymmetric tensor?

Best regards,
Andrey
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