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.
Kerr black hole in the formalism of isolated horizons
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abstract
We revise the work of Scholtz, Flandera and G\"urlebeck [Kerr-Newman black hole in the formalism of isolated horizons, Phys. Rev. D 96, 064024 (2017)]. We cast the Kerr metric explicitly in the form suitable for the framework of isolated horizons. We proceed in a geometrical fashion and are capable to provide the results in a compact closed manner, without any unevaluated integrals. We also discuss the uniqueness and drawbacks of this construction. We suggest a new vector field to generate the null geodesic foliation.
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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.