Exact algebraic separation of the gravitoelectromagnetic perturbations of Kerr-Newman-(anti-)de Sitter black holes
Abstract
We obtain an explicit separation of the coupled gravitational and electromagnetic radiative equations on nonextremal Kerr--Newman--(anti-)de Sitter black holes with nonzero charge and rotation. The construction uses a matrix with constant determinant, chosen independently of the frequency and azimuthal number, and treats the positive- and negative-spin sectors within the same formulation. We establish that this transformation is smooth and invertible throughout the open AdS exterior and between the event and cosmological horizons in dS. The resulting radial and angular systems are valid at arbitrary complex frequencies. We also express regularity of the radiative Newman--Penrose variables at the rotation axes and future horizons as conditions on the separated solutions. In the asymptotically flat limit, the transformation is related to Hintz's matrix integrating factor by the allowed frame freedom. These results provide a basis for studying quasinormal modes and black-hole stability in Kerr--Newman--(anti-)de Sitter spacetimes, as well as exploring holographic applications to strongly coupled systems.
Related
- Separation of variables for coupled radiative perturbations of Kerr-Newman-de Sitter black holes
- Perturbations of Kerr-Newman black holes: separation and mode stability
- Parity Isospectrality of the Kerr--Newman--de Sitter Black Hole
- Quasinormal modes of Kerr-Newman-de Sitter black holes from Heun connection formulae
- Perturbations of a Schwarzschild black hole and Newman-Unti gauge
BibTeX
@misc{zhao2026exact,
title = {{Exact algebraic separation of the gravitoelectromagnetic perturbations of Kerr-Newman-(anti-)de Sitter black holes}},
author = {Jun-Kun Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22274},
eprint = {2610.22274},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22274},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact algebraic separation of the gravitoelectromagnetic perturbations of Kerr-Newman-(anti-)de Sitter black holes
AU - Jun-Kun Zhao
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22274
UR - https://arxiv.org/abs/2610.22274
AB - We obtain an explicit separation of the coupled gravitational and electromagnetic radiative equations on nonextremal Kerr--Newman--(anti-)de Sitter black holes with nonzero charge and rotation. The construction uses a matrix with constant determinant, chosen independently of the frequency and azimuthal number, and treats the positive- and negative-spin sectors within the same formulation. We establish that this transformation is smooth and invertible throughout the open AdS exterior and between the event and cosmological horizons in dS. The resulting radial and angular systems are valid at arbitrary complex frequencies. We also express regularity of the radiative Newman--Penrose variables at the rotation axes and future horizons as conditions on the separated solutions. In the asymptotically flat limit, the transformation is related to Hintz's matrix integrating factor by the allowed frame freedom. These results provide a basis for studying quasinormal modes and black-hole stability in Kerr--Newman--(anti-)de Sitter spacetimes, as well as exploring holographic applications to strongly coupled systems.
ER -