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