  For very fast spinning black holes with a>0.9953 the orbital velocity of a
test particle unexpectly shows a positive radial gradient for low orbits, an
effect of GR which has been overlooked so far. For a=0.99616 the maximum radial
change of the orbital velocity equals the radial epicyclic frequency, which in
turn is in a 1:3 resonance with the vertical epicyclic frequency. Application
to Sgr A* using the quasi-periodic oscillations recently measured suggest that
the mass of Sgr A* is 3.28 +/- 0.13 million solar masses.
