The Einstein-Klein-Gordon Coupled System : Global Stability of the Minkowski Solution: (AMS-213) /

A definitive proof of global nonlinear stability of Minkowski spacetime as a solution of the Einstein-Klein-Gordon equationsThis book provides a definitive proof of global nonlinear stability of Minkowski spacetime as a solution of the Einstein-Klein-Gordon equations of general relativity. Along the...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Ionescu, Alexandru D. (Autor), Pausader, Benoît (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, [2022]
Colección:Annals of Mathematics Studies ; 403
Temas:
General relativity (Physics).
Klein-Gordon equation.
Mathematical physics.
Quantum field theory.
SCIENCE / Physics / Mathematical & Computational.
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 system.
Coordinate-free.
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.
Light cone.
Local coordinates.
Mathematical optimization.
Metric tensor (general relativity).
Metric tensor.
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.
Acceso en línea:Texto completo
Texto completo
Descripción
Sumario:A definitive proof of global nonlinear stability of Minkowski spacetime as a solution of the Einstein-Klein-Gordon equationsThis book provides a definitive proof of global nonlinear stability of Minkowski spacetime 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 spacetime, 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.
Descripción Física:1 online resource (308 p.)
ISBN:9780691233031
9783110993899
9783110994810
9783110993448
9783110993219
9783110749731
Acceso:restricted access

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