3:2 and/or 3:1 twin high frequency quasi-periodic oscillations ( HFQPOs ) have been measured for the three microquasars GRO J1655-40 , XTE J1550-564 and GRS 1915+105 .
For a test particle orbiting a rotating black on a stable circular orbit there exist two different orbits at which the vertical and radial epicyclic oscillations are in either a 3:1 or 3:2 parametric resonance for any choice of the black hole angular momentum a .
If the two orbits are required to be frequency commensurable Keplerian orbits there is only one solution for the two orbit radii and a .
This model predicts that the microquasars have the same a , and it predicts their black hole masses on the basis of the measured HFQPOs in agreement with the dynamically determined masses .
Application of this model to the Galactic Center black hole Sgr A* using the recently measured QPOs ( Genzel et al. , 2003 , Aschenbach et al. , 2004 ) leads to a black hole mass of ( 3.28 \pm 0.13 ) \times 10 ^ { 6 } M _ { \odot } , and the same a as for the microquasars .
The possibility that all four sources have a = 0.99616 suggests that this value is the upper limit of a imposed by general relativity .
The same value for the lower orbit radius and the same value for a are also suggested by an analysis of the general relativistic expression for the radial gradient of the orbital velocity , which changes sign in a narrow annular region around the lower orbit when a > 0.9953 .