The (in)stability of quasinormal modes of Boulware-Deser-Wheeler black hole in the hyperboloidal framework

Abstract

We study the quasinormal modes of Boulware-Deser-Wheeler black hole in Einstein-Gauss-Bonnet gravity theory within the hyperboloidal framework. The effective potentials for the test Klein-Gordon field and gravitational perturbations of scalar, vector, and tensor types are thoroughly investigated and put into several typical classes. The effective potentials for the gravitational perturbations have more diverse behaviors than those in general relativity, such as double peaks, the existence of the negative region adjacent to or far away from the event horizon, etc. These lead to the existence of unstable modes ($\text{Im}\omega <0$), and the presence of gravitational wave echoes. These rich phenomenons are inherent in Einstein-Gauss-Bonnet theory, rather than artificially introduced by hand. What's more, the (in)stability of quasinormal modes is studied in frequency domain and time domain, respectively. For the frequency-domain, the pseudospectrum is used to account for the instability of the spectrum. For the time-domain, we add a small bump to the effective potential, and find that the new waveform does not differ significantly from the original one, where the comparison is characterized by the so-called mismatch functions. This means that quasinormal modes are stable in time-domain regardless of the shapes of the original effective potentials. In this way, our study reveals the non-equivalence of the stability of quasinormal modes in the frequency-domain and the time-domain. Besides, we also numerically investigate Price's law at both finite distances and infinity with the assistance of the hyperboloidal approach.

29 pages, 14 figures; This revised version includes a new figure, corrected typos, and improved discussions. The manuscript has been accepted for publication as a regular article in SCPMA

References in corpus (35)

• Non-Hermitian Physics
• Can environmental effects spoil precision gravitational-wave astrophysics?
• Viscosity Bound and Causality Violation
• Destabilizing the Fundamental Mode of Black Holes: The Elephant and the Flea
• Hyperboloidal foliations and scri-fixing
• Static and symmetric wormholes respecting energy conditions in Einstein-Gauss-Bonnet gravity
• Agnostic black hole spectroscopy: Quasinormal mode content of numerical relativity waveforms and limits of validity of linear perturbation theory
• A geometric framework for black hole perturbations
• (In)stability of D-dimensional black holes in Gauss-Bonnet theory
• Higher order gravity theories and their black hole solutions
• Stability of the fundamental quasinormal mode in time-domain observations against small perturbations
• Astrophysical implications of hypothetical stable TeV-scale black holes
• Catastrophic Instability of Small Lovelock Black Holes
• Master Equations for Gravitational Perturbations of Static Lovelock Black Holes in Higher Dimensions
• Energy scales and black hole pseudospectra: the structural role of the scalar product
• Pseudospectrum of horizonless compact objects: a bootstrap instability mechanism
• Perturbing the perturbed: Stability of quasinormal modes in presence of a positive cosmological constant
• Ringdown stability: greybody factors as stable gravitational-wave observables
• Gravitational instability of static spherically symmetric Einstein-Gauss-Bonnet black holes in five and six dimensions
• Stability of Lovelock Black Holes under Tensor Perturbations
• Asymptotical quasinormal mode spectrum for piecewise approximate effective potential
• Pseudospectra of Holographic Quasinormal Modes
• Structural aspects of the anti-de Sitter black hole pseudospectrum
• Pseudospectrum of de Sitter black holes
• Quasinormal modes of Schwarzschild black holes on the real axis
• From black hole spectral instability to stable observables
• Hushing black holes: tails in dynamical spacetimes
• Spectral instability of black holes: relating the frequency domain to the time domain
• The quasinormal modes, pseudospectrum and time evolution of Proca fields in quantum Oppenheimer-Snyder-de Sitter spacetime
• On destabilising quasi-normal modes with a radially concentrated perturbation
• Hyperbolic times in Minkowski space
• Quasi-normal mode expansions of black hole perturbations: a hyperboloidal Keldysh's approach
• Pseudospectra of Quasinormal Modes and Holography
• Hyperbolicity and Causality of Einstein-Gauss-Bonnet Gravity in Warped Product Spacetimes
• Exact black hole solutions in higher-order scalar-tensor theories

Cited by in corpus (5)

• Pseudospectrum and time-domain analysis of the EFT corrected black holes
• QNM families: classification and competition
• Charged Scalar Field at Future Null Infinity via Nonlinear Hyperboloidal Evolution
• Pseudospectrum and (in)stability of black hole total transmission modes
• Quasinormal modes of regular black holes surrounded by skewed dark matter distributions