Projection azimutale
γ = φ, ρ = f(z), f(0) = 0
Equidistante
γ = φ, ρ = f(z) = z, f(0) = 0
Longitude γ = φ
ds2 = c2.dt2 − dr2 − r2.dγ2 − df(z)2 = 0
dt2 = dr2 + r2.dγ2 + dz2
So shape of time depends the position.....