where ( t , ρ ρ , ϕ ϕ , z ) are the cylindrical Weyl–Lewis–Papapetrou coordinates in 3 + 1 -dimensional spacetime, and λ λ , ν ν , ω ω , and B , are unknown functions of the spatial non-angular coordinates ρ ρ and z only. Different authors define the functions of the coordinates differently.