Eigenvalue repulsions and quasinormal mode spectra of Kerr-Newman: an extended study
arXiv:2205.13072 · doi:10.1007/JHEP07(2022)076
Abstract
The frequency spectra of the gravito-electromagnetic perturbations of the Kerr-Newman (KN) black hole with the slowest decay rate have been computed recently. It has been found that KN has two families the photon sphere and the near-horizon families of quasinormal modes (QNMs), which display the interesting phenomenon of eigenvalue repulsion. The perturbation equations, in spite of being a coupled system of two PDEs, are amenable to an analytic solution using the method of separation of variables in a near-horizon expansion around the extremal KN black hole. This leads to an analytical formula for the QNM frequencies that provides an excellent approximation to the numerical data near-extremality. In the present manuscript we provide an extended study of these properties that were not detailed in the original studies. This includes: 1) a full derivation of a gauge invariant system of two coupled PDEs that describes the perturbation equations \cite{Dias:2015wqa}, 2) a derivation of the eikonal frequency approximation \cite{Zimmerman:2015trm,Dias:2021yju} and its comparison with the numerical QNM data, 3) a derivation of the near-horizon frequency approximation \cite{Dias:2021yju} and its comparison with the numerical QNMs, and 4) more details on the phenomenon of eigenvalue repulsion (also known as \emph{level repulsion}, \emph{avoided crossing} or \emph{Wigner-Teller effect}) and a first principles understanding of it that was missing in the previous studies. Moreover, we provide the frequency spectra of other KN QNM families of interest to demonstrate that they are more damped than the ones we discuss in full detail.
64 pages, 31 figures
References in corpus (18)
- Advanced LIGO
- Quasinormal modes and Strong Cosmic Censorship
- Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation
- An instability of higher-dimensional rotating black holes
- Slow relaxation of rapidly rotating black holes
- The Quasinormal Mode Spectrum of a Kerr Black Hole in the Eikonal Limit
- Branching of quasinormal modes for nearly extremal Kerr black holes
- Linear mode stability of Kerr-Newman and its quasinormal modes
- Ultraspinning instability of rotating black holes
- A scalar field condensation instability of rotating anti-de Sitter black holes
- The Quasinormal Modes of Weakly Charged Kerr-Newman Spacetimes
- General relativistic simulations of the quasi-circular inspiral and merger of charged black holes: GW150914 and fundamental physics implications
- Constraints on Kerr-Newman black holes from merger-ringdown gravitational-wave observations
- Eigenvalue repulsions in the quasinormal spectra of the Kerr-Newman black hole
- Correspondence of eikonal quasinormal modes and unstable fundamental photon orbits for Kerr-Newman black hole
- Testing the nonlinear stability of Kerr-Newman black holes
- Sharp decay estimates for massless Dirac fields on a Schwarzschild background
- The origin of the Reissner-Nordström de Sitter instability