Vector perturbations of Kerr-AdS$_5$ and the Painlev\'e VI transcendent
Abstract
We analyze the Ansatz of separability for Maxwell equations in generically spinning, five-dimensional Kerr-AdS black holes. We find that the parameter \mu introduced in a previous work by O. Lunin can be interpreted as apparent singularities of the resulting radial and angular equations. Using isomonodromy deformations, we describe a non-linear symmetry of the system, under which \mu is tied to the Painlev\'e VI transcendent. By translating the boundary conditions imposed on the solutions of the equations for quasinormal modes in terms of monodromy data, we find a procedure to fix \mu and study the behavior of the quasinormal modes in the limit of fast spinning small black holes.
Keywords
Cite
@article{arxiv.2002.06108,
title = {Vector perturbations of Kerr-AdS$_5$ and the Painlev\'e VI transcendent},
author = {Julián Barragán-Amado and Bruno Carneiro da Cunha and Elisabetta Pallante},
journal= {arXiv preprint arXiv:2002.06108},
year = {2020}
}
Comments
Minor comments on fixing of parameters and polarizations, 31 pages, 2 figures, JHEP style