Gravitational Collider Physics via Pulsar-Black Hole Binaries II: Fine and Hyperfine Structures Are Favored

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 accompanied by 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.