Bernd Aschenbach (MPE)
I have revisited the theory of test-particles moving around rotating black holes (BHs) on stable circular free orbits. This theory is well established and meanwhile subject of numerous textbooks. But I discovered that for very fast spinning BHs the orbital velocity of the test-particle, unexpectedly, is not a monotonic function of the distance from the BH in contrast to the particle's total energy and angular momentum, for instance. A detailed analysis shows that at a well defined value of the BH spin the change of the orbital velocity per unit radial length, which is positive in a narrow radial annulus, equals the radial epicyclic frequency. Furthermore, at this radius the vertical and radial epicyclic frequencies show a 3:1 resonance, which I suggest to be associated with the twin high frequency quasi-periodic oscillations observed in a couple of galactic microquasars. Interestingly the quasi-periodicities recently discovered in NIR and X-ray flares of Sgr A* are also consistent with a 3:2:1 ratio. With the orbital radius and the BH spin fixed by this new effect of GR the BH mass can uniquely be calculated from just the observed frequencies. For the microquasars and Sgr A* the BH mass agrees quite well with the dynamically determined masses but with significantly less uncertainty.