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Title

A scattering theory for the linearised Einstein equations on the exterior of the Schwarzschild black hole: The Teukolsky equations.

Abstract

The Teukolsky equations of spin \pm2 are a pair of linear wave equations that arise in the study of the linearised Einstein equations on the Kerr family of black holes and govern certain components of the curvature components in a null frame. We develop a scattering theory for these equations on the exterior of the Schwarzschild black hole. We incorporate what is known in the literature as the Teukolsky–Starobinsky correspondence into our scattering statement as a step towards a scattering theory for the full system of linearised Einstein equations.

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