On scalar and electromagnetic perturbations of the root--Kerr object
Abstract
We study scalar and electromagnetic perturbations of the root--Kerr object. Its source-free exterior carries the electromagnetic field obtained in the vanishing-mass limit of the Kerr--Newman black hole, while its physical source is a rotating disk with an essential distributional rim contribution. For a massless charged scalar, the minimally coupled Klein--Gordon equation separates into a confluent-Heun (CHE) radial equation with a direct coupling between the scalar and background charges. We give the associated Nekrasov--Shatashvili (NS) dictionary and show that the disk is an ordinary radial point. For electromagnetic pertubations, we derive the equations for the radiative Newman--Penrose Maxwell scalars directly. They have the same confluent-Heun structure, but a Maxwell perturbation has no bulk coupling to the background potential. Charge-dependent photon scattering data therefore cannot be fixed by the exterior equation alone. We formulate the disk/rim boundary-data problem, identify the response data required to convert exact CHE/NS connection coefficients into a physical scattering matrix, and show how all-spin helicity-flip Compton information constrains the response on the radiative subspace. The analysis separates exact exterior propagation and amplitude matching from the additional source dynamics required for a microscopic response.
Related
- Time-domain analysis of scalar perturbations of Kerr--Newman black holes with Chern--Simons and Maxwell couplings
- Perturbations of Kerr-Newman black holes: separation and mode stability
- Charge-regular formulation and radiative amplitudes of Kerr-Newman perturbations
- Separation of variables for coupled radiative perturbations of Kerr-Newman-de Sitter black holes
- Exact algebraic separation of the gravitoelectromagnetic perturbations of Kerr-Newman-(anti-)de Sitter black holes
BibTeX
@misc{akhtar2026scalar,
title = {{On scalar and electromagnetic perturbations of the root--Kerr object}},
author = {Samim Akhtar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09191},
eprint = {2609.09191},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09191},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On scalar and electromagnetic perturbations of the root--Kerr object
AU - Samim Akhtar
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.09191
UR - https://arxiv.org/abs/2609.09191
AB - We study scalar and electromagnetic perturbations of the root--Kerr object. Its source-free exterior carries the electromagnetic field obtained in the vanishing-mass limit of the Kerr--Newman black hole, while its physical source is a rotating disk with an essential distributional rim contribution. For a massless charged scalar, the minimally coupled Klein--Gordon equation separates into a confluent-Heun (CHE) radial equation with a direct coupling between the scalar and background charges. We give the associated Nekrasov--Shatashvili (NS) dictionary and show that the disk is an ordinary radial point. For electromagnetic pertubations, we derive the equations for the radiative Newman--Penrose Maxwell scalars directly. They have the same confluent-Heun structure, but a Maxwell perturbation has no bulk coupling to the background potential. Charge-dependent photon scattering data therefore cannot be fixed by the exterior equation alone. We formulate the disk/rim boundary-data problem, identify the response data required to convert exact CHE/NS connection coefficients into a physical scattering matrix, and show how all-spin helicity-flip Compton information constrains the response on the radiative subspace. The analysis separates exact exterior propagation and amplitude matching from the additional source dynamics required for a microscopic response.
ER -