  The numerical investigation of Bondi-Hoyle accretion onto a moving black hole
has a long history, both in Newtonian and in general-relativistic physics. By
performing new two-dimensional and general-relativistic simulations onto a
rotating black hole, we point out a novel feature, namely, that quasi-periodic
oscillations (QPOs) are naturally produced in the shock cone that develops in
the downstream part of the flow. Because the shock cone in the downstream part
of the flow acts as a cavity trapping pressure perturbations, modes with
frequencies in the integer ratios 2:1 and 3:1 are easily produced. The
frequencies of these modes depend on the black-hole spin and on the properties
of the flow, and scale linearly with the inverse of the black-hole mass. Our
results may be relevant for explaining the detection of QPOs in Sagittarius A*,
once such detection is confirmed by further observations. Finally, we report on
the development of the flip-flop instability, which can affect the shock cone
under suitable conditions; such an instability has been discussed before in
Newtonian simulations but was never found in a relativistic regime.
