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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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Main Theorem

Main Theorem

(p.89) Chapter Three Main Theorem
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations

Sergiu Klainerman

Jérémie Szeftel

Princeton University Press

This chapter presents the main theorem, its main conclusions, as well as a full strategy of its proof, divided in nine supporting intermediate results, Theorems M0–M8. The chapter specifies the closeness to Schwarzschild of the initial data in the context of the Characteristic Cauchy problem. The conclusions of the main theorem can be immediately extended to the case where the data are specified to be close to Schwarzschild on a spacelike hypersurface Σ‎. The chapter then outlines the main bootstrap assumptions. It also provides a short description of the results concerning the General Covariant Modulation procedure, which is at the heart of the proof.

Keywords:   Schwarzschild spacetimes, spacelike hypersurface, bootstrap assumptions, General Covariant Modulation, Characteristic Cauchy problem

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