Pseudospectrum and black hole total transmission mode (in)stability

TL;DR

This paper investigates the spectral stability of total transmission modes in higher-dimensional black holes using pseudospectrum analysis, revealing that most TTMs are unstable except for specific purely imaginary modes.

Contribution

It introduces a pseudospectrum-based approach to analyze TTM stability and extends understanding of mode behavior across dimensions and spins in black hole spacetimes.

Findings

TTMs are generally spectrally unstable with higher sensitivity for overtones.

Purely imaginary TTMs are more stable and occur only for spin 2.

Genuinely complex TTMs appear only in dimensions d ≥ 8.

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 the 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 a purely imaginary TTM whose pseudospectrum's contours are nearly concentric and whose condition number is orders of magnitude smaller than that of the overtones, indicating enhanced spectral stability. Additionally, we confirm that purely imaginary TTMs occur only for spin $s=2$, whereas genuinely complex TTM families appear only in sufficiently high dimensions, $d \geqslant 8$, extending earlier claims that placed the onset at $d \geqslant 10$.