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Black-hole spectroscopy: quasinormal modes, ringdown stability and the pseudospectrum
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Black-hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation of multiple ringdown modes in gravitational waveforms could soon lead to high-precision gravitational-wave spectroscopy, thus it is critical to understand if the quasinormal mode spectrum itself is affected by astrophysical environments, quantum corrections, and other generic modifications. In this chapter, we will review the black-hole spectroscopy program and its challenges regarding quasinormal mode detection, the overtone status and the recent evidence that supports the existence of nonlinearities in the spectrum of black holes. We will then discuss a newly introduced non-modal tool in black-hole physics, namely the pseudospectrum; a mathematical notion that can shed light on the spectral stability of quasinormal modes, and discuss its novel applications in black holes and exotic horizonless compact objects. We will show that quasinormal modes generically suffer from spectral instabilities, explore how such phenomena can further affect black-hole spectroscopy, and discuss potential ringdown imprints and waveform stability issues in current and future gravitational-wave detectors.
Forward citations
Cited by 4 Pith papers
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Spectral instability of parametrized black hole quasinormal modes in the high-overtone limit via the exact WKB analysis
Constant 1/r⁴-or-higher parametrized corrections to the Regge–Wheeler potential drive the real part of high-overtone QNM frequencies to diverge (e.g., like N^{1/5}), unlike Schwarzschild.
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Pseudospectrum and (in)stability of black hole total transmission modes
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.
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Spectrum instability and greybody factor stability for parabolic approximation of Regge-Wheeler potential
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.
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Exceptional line and pseudospectrum in black hole spectroscopy
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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