Doran (2000) version of the Kerr-Newman metric:
ds2  =  - dt2 + [(r/R) dr + b (R/r) (dt - a sin2q df)]2 + r2 dq2 + R2 sin2q df2
where
R  º  (r2 + a2)1/2       r  º  (r2 + a2 cos2q)1/2       b  =  (2 M r - Q2)1/2 / R 
Space flowing and twisting into a Kerr black hole. River model of a rotating (Kerr-Newman) black hole

The Kerr-Newman river is a full 6-dimensional Lorentz river: it has a twist as well as a velocity.
(Hamilton & Lisle 2005)


  Penrose diagram of the charged (Reissner-Nordström) Black Hole