Linear mode stability of Kerr-Newman and its quasinormal modes

Abstract

We provide strong evidence that, up to $99.999\%$ of extremality, Kerr-Newman black holes (KN BHs) are linear mode stable within Einstein-Maxwell theory. We derive and solve, numerically, a coupled system of two PDEs for two gauge invariant fields that describe the most general linear perturbations of a KN BH (except for trivial modes that shift the parameters of the solution). We determine the quasinormal mode (QNM) spectrum of the KN BH as a function of its three parameters and find no unstable modes. In addition, we find that the QNMs that are connected continuously to the gravitational $\ell =m=2$ Schwarzschild QNM dominate the spectrum for all values of the parameter space ($m$ is the azimuthal number of the wave function and $\ell$ measures the number of nodes along the polar direction). Furthermore, all QNMs with $\ell =m$ approach Re$\omega =m{\Omega }_H^{ext}$ and Im$\omega =0$ at extremality; this is a universal property for any field of arbitrary spin $|s|\le 2$ propagating on a KN BH background ($\omega$ is the wave frequency and ${\Omega }_H^{ext}$ the BH angular velocity at extremality). We compare our results with available perturbative results in the small charge or small rotation regimes and find good agreement. We also present a simple proof that the Regge-Wheeler (odd) and Zerilli (even) sectors of Schwarzschild perturbations must be isospectral.

7 pages, 6 figures

References in corpus (8)

• An instability of higher-dimensional rotating black holes
• Slow relaxation of rapidly rotating black holes
• Branching of quasinormal modes for nearly extremal Kerr black holes
• A scalar field condensation instability of rotating anti-de Sitter black holes
• Ultraspinning instability of rotating black holes
• The Quasinormal Modes of Weakly Charged Kerr-Newman Spacetimes
• Testing the nonlinear stability of Kerr-Newman black holes
• A short remark (with a long title) on the universality of the quasinormal spectrum of near-extremal Kerr-Newman black holes

Cited by in corpus (37)

• The Science of the Einstein Telescope
• Parametrized ringdown spin expansion coefficients: a data-analysis framework for black-hole spectroscopy with multiple events
• An approach to computing spectral shifts for black holes beyond Kerr
• Constraints on Kerr-Newman black holes from merger-ringdown gravitational-wave observations
• Eigenvalue repulsions in the quasinormal spectra of the Kerr-Newman black hole
• Eigenvalue repulsions and quasinormal mode spectra of Kerr-Newman: an extended study
• Spectral method for metric perturbations of black holes: Kerr background case in general relativity
• Spectral Method for the Gravitational Perturbations of Black Holes: Schwarzschild Background Case
• Black hole superradiant instability for massive spin-2 fields
• Quasinormal modes of dilatonic Reissner-Nordström black holes
• Solving the Teukolsky equation with physics-informed neural networks
• Quasinormal modes of Kerr black holes using a spectral decomposition of the metric perturbations
• Spectral stability of near-extremal spacetimes
• Are slowly rotating Ellis-Bronnikov wormholes stable?
• Constraints on charged black holes from merger-ringdown signals in GWTC-3 and prospects for the Einstein Telescope
• Existence of Zero-damped Quasinormal Frequencies for Nearly Extremal Black Holes
• Identifying modified theories of gravity using binary black-hole ringdowns
• A Unified Spectral Approach for Quasinormal Modes of Lee-Wick Black Holes
• Quasinormal mode spectrum of rotating black holes in Einstein-Gauss-Bonnet-dilaton theory
• Spin-induced scalarization of Kerr-Newman black holes in Einstein-Maxwell-scalar theory
• Quasinormal modes of slowly rotating Kerr-Newman black holes using the double series method
• The fastest relaxation rate of higher-dimensional Reissner--Nordström black hole
• Binary dynamics from Einstein-Maxwell theory at second post-Newtonian order using effective field theory
• Theory-agnostic searches for non-gravitational modes in black hole ringdown
• Rotating black holes in valid vector-tensor theories after GW170817
• Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics
• Connecting quasi-normal modes with causality in Lovelock theories of gravity
• Kerr-Newman quasinormal modes and Seiberg-Witten theory
• Quasinormal modes of noncommutative geometry-inspired dirty black holes
• EFT Corrections to Charged Black Hole Quasinormal Modes
• Axial Gravitational Perturbations of Slowly-Rotating Compact Objects in General Relativity and Beyond
• Quasinormal modes of Kerr-Newman black holes: revisiting the Dudley-Finley approximation
• Quasinormal Mode Spectroscopy via Horizon-Brightened Quantum Optics
• QNM families: classification and competition
• Challenging theories of gravitation: dark matter, compact objects and gravitational waves
• Bounding dark charges on binary black holes using gravitational waves
• Computing the quasinormal modes and eigenfunctions for the Teukolsky equation using horizon penetrating, hyperboloidally compactified coordinates