For two-timescale perturbations about Kerr, the coarse-grained leading-order horizon shear vanishes and the angular-velocity and inaffinity corrections are uniform on each cut, defining adiabatic rigidity; the paper adds a gauge pipeline and charge-flux expansions for EMRI horizon absorption.
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Horizon flux-balance laws in the multiscale perturbation
For two-timescale perturbations about Kerr, the coarse-grained leading-order horizon shear vanishes and the angular-velocity and inaffinity corrections are uniform on each cut, defining adiabatic rigidity; the paper adds a gauge pipeline and charge-flux expansions for EMRI horizon absorption.