Holonomy invariance, orbital resonances and kilohertz QPOs

Quantized orbital structures are typical for many aspects of classical gravity (Newton's as well as Einstein's). The astronomical phenomenon of orbital resonances is a well-known example. Recently, Rothman et al (2001 Class. Quantum Grav. 18 1217-33) discussed quantized orbital structures in the novel context of a holonomy invariance of parallel transport in Schwarzschild geometry. We present here yet another example of quantization of orbits, one that is closely related to orbital resonances and closely analogous to holonomy invariance. This strong-gravity effect may have been already directly observed as the puzzling kilohertz quasi-periodic oscillations (QPOs) in the x-ray emission from a few accreting galactic black holes and several neutron stars.