  A rotating black hole causes the spin-axis of a nearby pulsar to precess due
to geodetic and gravitomagnetic frame-dragging effects. The aim of our
theoretical work here is to explore how this spin-precession can modify the
rate at which pulses are received on earth. Towards this end, we obtain the
complete evolution of the beam vectors of pulsars moving on equatorial circular
orbits in the Kerr spacetime, relative to asymptotic fixed observers. We
proceed to establish that such spin-precession effects can significantly modify
observed pulse frequencies and, in specific, we find that the observed pulse
frequency rises sharply as the orbit shrinks, potentially providing a new way
to locate horizons of Kerr black holes, even if observed for a very short time
period. We also discuss implications for detections of sub-millisecond pulsars,
pulsar nulling, quasi-periodic oscillations, multiply-peaked pulsar Fourier
profiles and how Kerr black holes can potentially be distinguished from naked
singularities.
