An exceptional-point framework for black-hole ringdown characterizes resonances near avoided crossings, demonstrates enhanced mode contributions in the time domain, and identifies the EP frequency as the physically relevant observable.
Pseudospectrum and binary black hole merger transients
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Bilinear products for black hole quasinormal modes on hyperboloidal foliations are divergent due to CPT transformations but can be regularized to define orthogonal modes and excitation coefficients.
Excitation factors of long-lived quasinormal modes in horizonless compact objects scale with their small imaginary frequency, suppressing early contributions and producing a hierarchy where prompt ringdown uses ordinary modes and late echoes use cavity modes.
In asymmetric Damour-Solodukhin wormholes, reflectionless and echo modes share asymptotic spectral properties parallel to the real frequency axis with matching spacing, and reflectionless modes lie closer to the axis yielding larger echo amplitudes.
High-frequency quasi-reflectionless scattering modes in the greybody factors of ultracompact horizonless objects are responsible for echoes in the time-domain response.
A review summarizing the state of the art in black hole quasinormal modes, ringdown waveform modeling, current LIGO-Virgo-KAGRA observations, and prospects for LISA and next-generation detectors.
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Bilinear products and the orthogonality of quasinormal modes on hyperboloidal foliations
Bilinear products for black hole quasinormal modes on hyperboloidal foliations are divergent due to CPT transformations but can be regularized to define orthogonal modes and excitation coefficients.