Spinning black holes and boson clouds
A spinning black hole can hand some of its rotational energy to a wave that circles it more slowly than its horizon turns. Start with that picture, work through the units and the conserved flux, recompute a published table yourself, and then read how a frontier paper turns growing clouds into limits on new particles.
L1 · Concept
Why can a spinning black hole make the waves around it ever stronger?
A wave that circles a spinning black hole more slowly than its horizon turns comes back stronger, paid for by the hole's rotation.
L1 · Chapter
Waves, spin and the scales of a Kerr black hole
Set up the units, horizon, horizon rotation and wave angular momentum, then derive when a wave can gain energy and when a light field is trapped.
L2 · Chapter
Conserved flux, physical units and a first growth estimate
Use the conserved wave flux to prove the gain condition, convert geometric units to seconds and electronvolts, and estimate a cloud's growth rate.
L3 · Chapter
Solving for the bound cloud's growth rate reproducibly
Find the cloud's complex frequency with a continued fraction, test convergence, avoid converging to the wrong overtone, and compare with a published table.
L3 · Method
Recomputing a published superradiance amplification table
Download the authors' scalar amplification table, recompute the spin 0.99 slice with an independent solver, and see where the hydrogenic growth formula holds.
L3 · Paper guide
How self-interactions change boson-cloud limits from spins and gravitational waves
Read Baryakhtar et al. 2021 figure by figure: which spin limits rest on measurements, which wave signals are projections, and what is still open.