  A rotating black hole can be clouded by light bosons via superradiance, and
thus acquire an atom-like structure. If such a gravitational atom system is
companioned with a pulsar, the pulsar can trigger transitions between energy
levels of the gravitational atom, and these transitions can be detected by
pulsar timing. We show that in such pulsar-black hole systems, fine and
hyperfine structure transitions are more likely to be probed than the Bohr
transition. Also, the calculation of these fine and hyperfine structure
transitions are under better analytic control. Thus, these fine and hyperfine
structure transitions are more ideal probes in the search for gravitational
collider signals in pulsar-black hole systems.
