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arXiv · 2211.07462

A Scattering Theory for Linearised Gravity on the Exterior of the Schwarzschild Black Hole II: The Full System

Hamed Masaood
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Abstract

We construct a scattering theory for the linearised Einstein equations on a Schwarzschild background in a double null gauge. We build on the results of Part I \cite{Mas20}, where we used the energy conservation enjoyed by the Regge--Wheeler equation associated with the stationarity of the Schwarzschild background to construct a scattering theory for the Teukolsky equations of spin $\pm2$. We now extend the scattering theory of Part I to the full system of linearised Einstein equations by treating it as a system of transport equations which is sourced by solutions to the Teukolsky equations, leading to Hilbert space-isomorphisms between spaces of finite energy initial data and corresponding spaces of scattering states under suitably chosen gauge conditions on initial and scattering data. As a corollary, we show that for a solution which is Bondi-normalised at both past and future null infinity, past and future linear memories are related by an antipodal map.

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Hamed Masaood. 2022-11-14. A Scattering Theory for Linearised Gravity on the Exterior of the Schwarzschild Black Hole II: The Full System. https://arxiv.org/abs/2211.07462

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