Darboux transformation in black hole perturbation theory

@article{Glampedakis2017DarbouxTI,
  title={Darboux transformation in black hole perturbation theory},
  author={Kostas Glampedakis and Aaron D. Johnson and Daniel J. Kennefick},
  journal={Physical Review D},
  year={2017},
  volume={96},
  pages={024036}
}
The Darboux transformation between ordinary differential equations is a 19th century technique that has seen wide use in quantum theory for producing exactly solvable potentials for the Schrodinger equation with specific spectral properties. In this paper we show that the same transformation appears in black hole theory, relating, for instance, the Zerilli and Regge-Wheeler equations for axial and polar Schwarzschild perturbations. The transformation reveals these two equations to be… 

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