Pseudospectrum and (in)stability of black hole total transmission modes

Abstract

Total transmission modes (TTMs) are modes with complex frequencies that propagate across a black hole spacetime without reflection. Recently, it is found that suitably tailored time-dependent scattering can excite these complex modes and suppress the reflected signal for the entire duration of the process, a phenomenon referred to as virtual absorption. Motivated by this, we present a study of the spectrum stability of TTMs using pseudospectrum and condition numbers. We focus on perturbations of $d$-dimensional Tangherlini black holes and recast the TTM problem as a generalized eigenvalue problem by utilizing the Eddington-Finkelstein coordinates. The results show that TTMs are generically spectrally unstable, with sensitivity increasing for higher overtones, in close analogy with quasinormal modes. A notable exception is the purely imaginary TTM in the positive imaginary axis in higher dimensions. Its pseudospectrum contours are nearly concentric, and its condition number is orders of magnitude smaller than those of the overtones, indicating enhanced spectral stability. As the spacetime dimension decreases, the condition number grows and becomes much larger in four dimensions in both the energy norm and the $L^2$ norm, suggesting possible spectral instability, although a definitive cross-dimensional conclusion is limited by the lack of a uniform physically preferred norm. Additionally, we confirm that purely imaginary TTMs occur for gravitational vector perturbations, whereas genuinely complex TTM families appear only in sufficiently high dimensions, $d⩾8$, extending earlier claims that placed the onset at $d⩾10$.

revtex4, 13 pages, 4 figures; title changed, expanded discussion of the four-dimensional case, norm dependence, pseudospectrum convergence, and related issues; accepted by PRD

References in corpus (25)

• Coherent Perfect Absorbers: Time-reversed Lasers
• Gravitational Perturbations of Higher Dimensional Rotating Black Holes: Tensor Perturbations
• An instability of higher-dimensional rotating black holes
• Gravitational perturbations of the Kerr geometry: High-accuracy study
• A geometric framework for black hole perturbations
• Ultraspinning instability of rotating black holes
• Pseudospectrum of horizonless compact objects: a bootstrap instability mechanism
• Stability of Five-dimensional Myers-Perry Black Holes with Equal Angular Momenta
• Perturbing the perturbed: Stability of quasinormal modes in presence of a positive cosmological constant
• Spectral (in)stability of quasinormal modes and strong cosmic censorship
• Hyperboloidal approach for static spherically symmetric spacetimes: a didactical introduction and applications in black-hole physics
• Pseudospectra of Holographic Quasinormal Modes
• Structural aspects of the anti-de Sitter black hole pseudospectrum
• Asymptotic Spectroscopy of Rotating Black Holes
• Pseudospectrum of de Sitter black holes
• Greybody factors, reflectionless scattering modes, and echoes of ultracompact horizonless objects
• Accurate Quasinormal Modes of the Five-Dimensional Schwarzschild-Tangherlini Black Holes
• Modes of the Kerr geometry with purely imaginary frequencies
• Transient dynamics of quasinormal mode sums
• Pseudospectrum of rotating analog black holes
• Pseudospectra of Quasinormal Modes and Holography
• The (in)stability of quasinormal modes of Boulware-Deser-Wheeler black hole in the hyperboloidal framework
• Pseudospectrum and time-domain analysis of the EFT corrected black holes
• Complete quasinormal modes of Type-D black holes
• New total transmission modes of the Kerr geometry with Schwarzschild limit frequencies at complex infinity