2026/07/16 by Yi-kun Li
#astro-ph.GA #gr-qc #hep-ph
Rotating black holes can bind ultralight bosons in macroscopic clouds whose level structure is swept by the tidal field of a binary companion. Existing estimates of the resulting resonant transitions have largely used hydrogenic wave functions, even where the cloud grows most efficiently and the Kerr geometry appreciably deforms its quasibound states. I compute tidal transition matrix elements on the numerically determined saturation branches of the |211⟩, |322⟩, and |433⟩ clouds. The calculation combines Kerr quasibound modes, their relativistic bilinear normalization, and an adiabatic uadrupolar perturbation of the Kerr metric. Across five Δm=-2 channels, the relativistic matrix element differs from its hydrogenic value by as much as 21.67%. Corrections above 10% persist when 99% of the cloud lies within 7% of the orbital separation. A component-resolved comparison attributes 78.7-82.5% of the logarithmic change to the radial mode profile and 13.3-16.2% to the bilinear normalization; the relativistic tidal geometry supplies a smaller additional correction. Exact Newtonian multipoles and an independent complex-contour construction confirm the quadrupole matrix elements. For resonances with intermediate Landau--Zener adiabaticity, the corrected matrix elements change the predicted cloud depletion by up to 13.7%. Relativistic cloud structure is therefore quantitatively important for binary histories that cross saturated-cloud resonances.