Horizon exchange and the universal all-spin response of Kerr
Abstract
The radial Teukolsky equation is invariant under exchange of the outer and inner horizons, although the physical boundary condition is not. We derive an exact monodromy relation between the corresponding Mano--Suzuki--Takasugi (MST) near-zone responses. At leading order in frequency and to all orders in spin, this relation yields, for every multipole, an expression for the leading horizon-exchange-odd response. For gravitational perturbations, it determines the exchange-odd contribution to quadrupolar absorption and organizes the exchange-even dynamical response into a digamma function whose expansion accounts for the odd- and even-zeta structures found in Kerr-Compton calculations. The exact relation, rather than the individual previously known small-spin coefficients, is the central result.
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BibTeX
@misc{vanhove2026horizon,
title = {{Horizon exchange and the universal all-spin response of Kerr}},
author = {Pierre Vanhove},
howpublished = {HAL},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05054},
eprint = {2611.05054},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05851234v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Horizon exchange and the universal all-spin response of Kerr
AU - Pierre Vanhove
PY - 2026
DA - 2026/11/03
PB - HAL
DO - 10.48550/arxiv.2611.05054
UR - https://hal.science/hal-05851234v1
AB - The radial Teukolsky equation is invariant under exchange of the outer and inner horizons, although the physical boundary condition is not. We derive an exact monodromy relation between the corresponding Mano--Suzuki--Takasugi (MST) near-zone responses. At leading order in frequency and to all orders in spin, this relation yields, for every multipole, an expression for the leading horizon-exchange-odd response. For gravitational perturbations, it determines the exchange-odd contribution to quadrupolar absorption and organizes the exchange-even dynamical response into a digamma function whose expansion accounts for the odd- and even-zeta structures found in Kerr-Compton calculations. The exact relation, rather than the individual previously known small-spin coefficients, is the central result.
ER -