Special relativity and the pseudo-Newtonian potential
  A simple re-scaling of velocities calculated from the Paczy{\'n}ski \& Wiita (1980) pseudo-Newtonian potential makes them consistent with special relativity and greatly improves the agreement with the exact relativistic calculations. The improvement is relevant in calculations of the Doppler effect, spectra and radiation transfer which all involve effects of special relativity. 
Marek A. Abramowicz, Andrei M. Beloborodov, Xingming Chen, and Igor V.   Igumenshchev