Essential mathematical insights into one of the most important and
challenging open problems in general relativity—the stability of
black holes One 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 Jérémie 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.
General
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