  We continue our earlier studies of quasi-periodic oscillations (QPOs) in the
power spectra of accreting, rapidly-rotating black holes that originate from
the geometric "light echoes" of X-ray flares occurring within the black hole
ergosphere. Our present work extends our previous treatment to
three-dimensional photon emission and orbits to allow for arbitrary latitudes
in the positions of the distant observers and the X-ray sources in place of the
mainly equatorial positions and photon orbits of the earlier consideration.
Following the trajectories of a large number of photons we calculate the
response functions of a given geometry and use them to produce model light
curves which we subsequently analyze to compute their power spectra and
autocorrelation functions. In the case of an optically-thin environment,
relevant to advection-dominated accretion flows, we consistently find QPOs at
frequencies of order of ~kHz for stellar-mass black hole candidates while order
of ~mHz for typical active galactic nuclei (~10^7 Msun) for a wide range of
viewing angles (30 to 80deg) from X-ray sources predominantly concentrated
toward the equator within the ergosphere. As in our previous treatment, here
too, the QPO signal is produced by the frame-dragging of the photons by the
rapidly-rotating black hole, which results in photon "bunches" separated by
constant time-lags, the result of multiple photon orbits around the hole. Our
model predicts for various source/observer configurations the robust presence
of a new class of QPOs, which is inevitably generic to curved spacetime
structure in rotating black hole systems.
