Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations

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Sergiu Klainerman Jérémie Szeftel

Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations

Sergiu Klainerman, Jérémie Szeftel

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English

Princeton University Press
22 February 2021

Non-Euclidean geometry; Relativity physics

Series: Annals of Mathematics Studies

Essential mathematical insights into one of the most important and challenging open problems in general relativity-the stability of black holesOne of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations. An affirmative answer to this question would provide strong theoretical support for the physical reality of black holes. In this book, Sergiu Klainerman and Jeremie Szeftel take a first important step toward solving the fundamental black hole stability problem in general relativity by establishing the stability of nonrotating black holes-or Schwarzschild spacetimes-under so-called polarized perturbations. This restriction ensures that the final state of evolution is itself a Schwarzschild space. Building on the remarkable advances made in the past fifteen years in establishing quantitative linear stability, Klainerman and Szeftel introduce a series of new ideas to deal with the strongly nonlinear, covariant features of the Einstein equations. Most preeminent among them is the general covariant modulation (GCM) procedure that allows them to determine the center of mass frame and the mass of the final black hole state. Essential reading for mathematicians and physicists alike, this book introduces a rich theoretical framework relevant to situations such as the full setting of the Kerr stability conjecture.

By: Sergiu Klainerman, Jérémie Szeftel
Imprint: Princeton University Press
Country of Publication: United States
Dimensions: Height: 254mm, Width: 178mm,
ISBN: 9780691212432
ISBN 10: 0691212430
Series: Annals of Mathematics Studies
Pages: 856
Publication Date: 22 February 2021
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Active

Sergiu Klainerman is Eugene Higgins Professor of Mathematics at Princeton University. His books include The Global Nonlinear Stability of the Minkowski Space (Princeton). Jeremie Szeftel is a CNRS senior researcher in mathematics at the Laboratoire Jacques-Louis Lions of Sorbonne Universite in Paris.