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Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations
Sergiu Klainerman, Jérémie Szeftel
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
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Einstein tensor, Cauchy problem, Einstein field equations, Initial value problem, Linear differential equation, Special case, Curvature, Metric tensor (general relativity), Orbital stability, Existential quantification, Riemann curvature tensor, Center of mass (relativistic), Lagrangian (field theory), Variable (mathematics), Gauge theory, Simultaneous equations, Null vector, Error term, Curvature invariant (general relativity), Ricci curvature, Conjecture, Estimation, Wave equation, Schwarzschild metric, Space form, Photon sphere, Stationary spacetime, Integration by parts, Eigenvalues and eigenvectors, Symmetry group, Hodge dual, Equation, Cosmological constant, Foliation, Partial differential equation, Compactification (mathematics), General relativity, A priori estimate, Hypersurface, Stress–energy tensor, Linear stability, Nonlinear system, Covariant derivative, Linearization, Null hypersurface, Geodesic, Kerr metric, Theorem, Scalar curvature, Tangent space, Derivative, Lie derivative, Three-dimensional space (mathematics), Pseudo-Riemannian manifold, Curvature tensor, Renormalization, Schwarzschild coordinates, Geodesics in general relativity, Quantity, Coefficient, Lyapunov stability, Cauchy horizon, Initial value formulation (general relativity), Lorentz transformation, Transition function, Minkowski space, Monotonic function, Exterior (topology), Linear equation, Vector field