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Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations(AMS-210)$
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Jérémie Szeftel and Sergiu Klainerman

Print publication date: 2020

Print ISBN-13: 9780691212425

Published to Princeton Scholarship Online: May 2021

DOI: 10.23943/princeton/9780691212425.001.0001

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Decay Estimates for α‎ and α‎ (Theorems M2, M3)

Decay Estimates for α‎ and α‎ (Theorems M2, M3)

(p.264) Chapter Six Decay Estimates for α‎ and α‎ (Theorems M2, M3)
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations

Sergiu Klainerman

Jérémie Szeftel

Princeton University Press

This chapter investigates the proof for Theorems M2 and M3. It relies on the decay of q to prove the decay estimates for α‎ and α‎. More precisely, the chapter relies on the results of Theorem M1 to prove Theorem M2 and M3. In Theorem M1, decay estimates are derived for q defined with respect to the global frame constructed in Proposition 3.26. To recover α‎ from q, the chapter derives a transport equation for α‎ where q is on the RHS. It then derives as Teukolsky–Starobinsky identity a parabolic equation for α‎. The chapter also improves bootstrap assumptions for α‎.

Keywords:   Theorem M2, Theorem M3, decay estimates, global frame, transport equation, Teukolsky–Starobinsky identity, parabolic equation, bootstrap assumptions

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