Jump to ContentJump to Main Navigation
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations(AMS-210)$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 21 May 2022

Preliminaries

Preliminaries

Chapter:
(p.24) Chapter Two Preliminaries
Source:
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations
Author(s):

Sergiu Klainerman

Jérémie Szeftel

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691212425.003.0002

This chapter discusses the main quantities, equations, and basic tools needed in the following chapters. It is the main reference kit providing all main null structure and null Bianchi equations, in general null frames, in the context of axially symmetric polarized spacetimes. The chapter translates the null structure and null Bianchi identities associated to an S-foliation in the reduced picture. It starts with general, Z-invariant, S-foliation, before considering the special case of geodesic foliations. The chapter then looks at perturbations of Schwarzschild and invariant quantities. It investigates how the main Ricci and curvature quantities change relative to frame transformations, i.e., linear transformations which take null frames into null frames. Finally, the chapter presents wave equations for the invariant quantities.

Keywords:   null structure equations, null Bianchi equations, null frames, axially symmetric polarized spacetimes, geodesic foliations, Schwarzschild spacetimes, invariant quantities, wave equations

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.