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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 (Theorems M4, M5)

Decay Estimates (Theorems M4, M5)

(p.295) Chapter Seven Decay Estimates (Theorems M4, M5)
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations

Sergiu Klainerman

Jérémie Szeftel

Princeton University Press

This chapter evaluates the proof for Theorems M4 and M5. It relies on the decay of q, α‎ and α‎ to prove the decay estimates for all the other quantities. More precisely, the chapter relies on the results of Theorems M1, M2, and M3 to prove Theorems M4 and M5. The detailed proof of Theorem M4 provides the main decay estimates in (ext)M. The proof depends in a fundamental way on the geometric properties of the GCM hypersurface Σ‎∗, the spacelike future boundary of (ext)M introduced in section 3.1.2. The chapter then reformulates the main bootstrap assumptions in the form needed in the proof of Theorem M4.

Keywords:   Theorem M4, Theorem M5, decay estimates, GCM hypersuface, bootstrap assumptions

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