Decomposition of tensors with xAct

[ma_fede]

Hello,

I would like to understand if it is possible to do the following with the package xAct.
Imagine I am given the Schwarzschild metric, with its timelike killing field T. I define the electric and magnetic components of the Maxwell field to be
E_alpha := F_{alpha beta} T^{beta},
B_alpha := *F_{alpha beta} T^{beta},
where * denotes the hodge dual, and F is a two antisymmetric covariant tensorfield.
I am given an expression containing contractions of the tensorfield F with itself (say U = F^{alpha beta} F_{alpha beta}).

I would like to know if there is a way of expressing U in terms of E and B, with xAct. Any help would be much appreciated.
Best,

Fede

[Thomas Bäckdahl]

Hi Fede,

Yes, it is possible. See the attached notebook.

Regards
Thomas

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[ma_fede]

Dear Thomas,

that was really helpful. Thank you.
Best,

Fede