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Pseudospectra of complex momentum modes

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arxiv 2407.06104 v1 pith:3F4NDZQP submitted 2024-07-08 hep-th gr-qc

David Garcia-Fariña , Karl Landsteiner , Pau G. Romeu , Pablo Saura-Bastida This is my paper · ORCID
classification hep-thgr-qc
keywords modescomplexmomentumpseudospectraquasinormalblackfrequencyholes
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We initiate the study of stability and pseudospectra of complex momentum modes of asymptotically anti-de Sitter black holes. Similar to quasinormal modes, these can be defined as the poles of the holographic Green's function, albeit for real frequency and complex momentum. Their pseudospectra are in stark contrast to the pseudospectra of quasinormal modes of AdS black holes. Contrary to the case of quasinormal mode pseudospectra, the resolvent is well-defined, and the numerical approximation shows fast convergence. At zero frequency, complex momentum modes are stable normal modes of a Hermitian operator. Even for large frequencies, they show only comparatively mild spectral instability. We also find that local potential perturbations cannot destabilize the lowest complex momentum mode.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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

    gr-qc 2025-12 conditional novelty 6.0 of 10

    Total transmission modes of Tangherlini black holes are generically spectrally unstable, except for a purely imaginary gravitational mode with nearly concentric pseudospectrum; complex TTM families appear already at d=8.

  2. Spectrum instability and greybody factor stability for parabolic approximation of Regge-Wheeler potential

    gr-qc 2025-05 conditional novelty 6.0 of 10

    Replacing the Regge-Wheeler potential by piecewise parabolas makes quasinormal-mode spectra unstable, with long-lived overtones, while greybody factors stay close to the exact Schwarzschild result.

  3. Exceptional line and pseudospectrum in black hole spectroscopy

    gr-qc 2025-11 conditional novelty 5.0 of 10

    A continuous line of exceptional points exists in the three-parameter space of a Gaussian-bump-perturbed Regge-Wheeler potential, with pseudospectral contour sizes scaling as ε^{1/2} at second-order EPs.

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