Hyperboloidal Method for Quasinormal Modes of Non-Relativistic Operators

TL;DR

This paper extends the hyperboloidal method, originally used in relativistic contexts, to non-relativistic quantum systems like the Schrödinger equation, enabling new calculations of quasinormal modes relevant for black hole spectroscopy.

Contribution

The authors adapt the hyperboloidal method for non-relativistic operators, broadening its applicability to quantum mechanics and bound-state problems.

Findings

Successfully computed non-relativistic quasinormal modes

Demonstrated method's utility for Schrödinger equation

Provided insights into black hole spectroscopy applications

Abstract

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.