A definitive proof of global nonlinear stability of Minkowski
space-time as a solution of the Einstein-Klein-Gordon equations
This book provides a definitive proof of global nonlinear stability of
Minkowski space-time as a solution of the Einstein-Klein-Gordon
equations of general relativity. Along the way, a novel robust
analytical framework is developed, which extends to more general matter
models. Alexandru Ionescu and Benoît Pausader prove global regularity at
an appropriate level of generality of the initial data, and then prove
several important asymptotic properties of the resulting space-time,
such as future geodesic completeness, peeling estimates of the Riemann
curvature tensor, conservation laws for the ADM tensor, and Bondi energy
identities and inequalities.
The book is self-contained, providing complete proofs and precise
statements, which develop a refined theory for solutions of quasilinear
Klein-Gordon and wave equations, including novel linear and bilinear
estimates. Only mild decay assumptions are made on the scalar field and
the initial metric is allowed to have nonisotropic decay consistent with
the positive mass theorem. The framework incorporates analysis both in
physical and Fourier space, and is compatible with previous results on
other physical models such as water waves and plasma physics.