The bound states of the inverted Regge-Wheeler potential are exponentially condensed near zero energy and strongly delocalized, linking black hole overtone instability to long-range potential features.
Hyperboloidal Method for Quasinormal Modes of Non-Relativistic Operators
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The recently reported compactified hyperboloidal method has found wide use in the numerical computation of quasinormal modes, with implications for fields as diverse as gravitational physics and optics. We extend this intrinsically relativistic method into the non-relativistic domain, demonstrating its use to calculate the quasinormal modes of the Schr\"odinger equation and solve related bound-state problems. We also describe how to further generalize this method, offering a perspective on the importance of non-relativistic quasinormal modes for the programme of black hole spectroscopy.
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Bound States of the Schwarzschild Black Hole
The bound states of the inverted Regge-Wheeler potential are exponentially condensed near zero energy and strongly delocalized, linking black hole overtone instability to long-range potential features.