The Einstein-Klein-Gordon Coupled System (eBook)

Global Stability of the Minkowski Solution

Alexandru D. Ionescu, Benoît Pausader (Autoren)

eBook Download: PDF

2022
308 Seiten
Princeton University Press (Verlag)
978-0-691-23303-1 (ISBN)

Infos

A definitive proof of global nonlinear stability of Minkowski space-time as a solution of the Einstein-Klein-Gordon equationsThis 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 Benoit 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.

Produkt-Details

• Erscheint lt. Verlag: 15.3.2022
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Schlagworte: Addition • Algebraic Structure • Antiderivative • Approximation • Asymptote • asymptotic analysis • Bending • Big O notation • Bootstrapping (statistics) • Calculation • Cauchy distribution • coefficient • combination • Compact space • complex number • Computation • Conserved quantity • Coordinate-free • coordinate system • covariant derivative • Derivative • Differential operator • dispersion relation • Einstein Field Equations • energy functional • Equation • estimation • exponential growth • foliation • fourier analysis • Fourier transform • Function (mathematics) • function space • General relativity • geodesic • Geodesics in general relativity • Geographic coordinate system • Geometry • Global Analysis • globality • High Frequency • Hyperboloid • hypersurface • hypothesis • implementation • ingredient • Integration by parts • Interpolation inequality • Klein–Gordon equation • light cone • Local coordinates • Mathematical Optimization • Metric tensor • Metric tensor (general relativity) • Minkowski space • Momentum • Monograph • Monotonic Function • nonlinear system • Optics • parametrization • partial differential equation • Pointwise • Poisson Bracket • Quantity • remainder • result • Riemann curvature tensor • Scalar Field • scattering • Schwarzschild metric • scientific notation • Second fundamental form • Simultaneous Equations • Small data • small number • Sobolev Space • Soliton • space • Stability Theory • Stress–energy tensor • Support (mathematics) • symmetrization • Theorem • time derivative • Timelike Infinity • Trace (linear algebra) • two-dimensional space • Vacuum • Vector field • Very Low Frequency
• ISBN-10: 0-691-23303-9 / 0691233039
• ISBN-13: 978-0-691-23303-1 / 9780691233031