Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension

Understand

We consider time reversal transformations to obtain twofold orthogonal splittings of any tensor on a Lorentzian space of arbitrary dimension n.

• Applied to the Weyl tensor of a spacetime, this leads to a definition of its electric and magnetic parts relative to an observer (i.e., a unit timelike vector field u), in any n.
• We study the cases where one of these parts vanishes in particular, i.e., purely electric (PE) or magnetic (PM) spacetimes.
• We generalize several results from four to higher dimensions and discuss new features of higher dimensions.