Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations: (AMS-210)

Sergiu Klainerman and Jérémie Szeftel take a first step toward solving the fundamental black hole stability problem in general relativity by establishing the stability of nonrotating black holes under polarized perturbations. This restriction ensures that the final state of evolution is itself a Schwarzschild space.

Format: Paperback / softback
Length: 856 pages
Publication date: 15 December 2020
Publisher: Princeton University Press

One of the most important and challenging open problems in general relativity is the stability of black holes. This question is crucial in understanding the physical reality of black holes, as a positive answer would provide strong theoretical support for their existence. In this book, Sergiu Klainerman and Jérémie Szeftel take a significant step towards 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 prominent among them is the general covariant modulation (GCM) procedure, which allows them to determine the center of mass frame and the mass of the final black hole state.

This book is essential reading for mathematicians and physicists alike, as it introduces a rich theoretical framework relevant to situations such as the full setting of the Kerr stability conjecture. The authors' work provides a solid foundation for further research in this field and has the potential to shed light on the mysterious behavior of black holes.

Weight: 1606g
Dimension: 178 x 255 x 49 (mm)
ISBN-13: 9780691212425