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The Global Nonlinear Stability of the Minkowski Space (PMS-41)
Sergiu Klainerman, Demetrios Christodoulou
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter.
Originally published in 1994.
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Foliation, Einstein field equations, Exponential map (Riemannian geometry), Lorentz group, Covariant derivative, Uniformization theorem, Partial derivative, Existential quantification, Homotopy, Scalar curvature, Orthonormal basis, Sard's theorem, Coefficient, Null hypersurface, Metric tensor, Diffeomorphism, Theorem, Logarithm, Existence theorem, Isoperimetric inequality, Projection (linear algebra), Nonlinear system, Weyl tensor, Cut locus (Riemannian manifold), Linear map, Minkowski space, Sobolev space, Curvature, Differentiable function, Riemann surface, Scale invariance, Trace (linear algebra), Normal (geometry), Eigenvalues and eigenvectors, Hyperbolic partial differential equation, Cauchy–Riemann equations, Degeneracy (mathematics), Stokes' theorem, Schwarzschild metric, Tangent space, Riemannian manifold, Quantity, Angular momentum operator, Eikonal equation, Estimation, Equation, Exterior (topology), Infinitesimal generator (stochastic processes), Laplace's equation, Vector field, Hypersurface, Mass formula, Symmetric tensor, Asymptotic analysis, Curvature tensor, Integral curve, Linear equation, Boundary value problem, Poisson's equation, Second fundamental form, Riemannian geometry, Riemann curvature tensor, Sobolev inequality, Lie derivative, Hodge dual, Radial function, Comparison theorem, Geodesics in general relativity, Derivative, Ricci curvature