Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations (eBook)

Sergiu Klainerman, Jeremie Szeftel (Autoren)

eBook Download: PDF

2020
856 Seiten
Princeton University Press (Verlag)
978-0-691-21852-6 (ISBN)

Infos

Essential mathematical insights into one of the most important and challenging open problems in general relativity-the stability of black holesOne 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 Jeremie 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.

Produkt-Details

• Erscheint lt. Verlag: 15.12.2020
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Zusatzinfo: 13 b/w illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Relativitätstheorie
• Schlagworte: analytic function • Angular momentum • A priori estimate • asymptotic stability • Bianchi Identities • Big O notation • boundedness • Calculation • Cauchy distribution • Cauchy horizon • Cauchy problem • Causal structure • Center of mass (relativistic) • coefficient • coercivity • commutator • Compactification (mathematics) • conjecture • convection–diffusion equation • coordinate system • cosmic censorship • cosmological constant • covariant derivative • Curvature • curvature components • Curvature invariant (general relativity) • Curvature tensor • Decay estimates • Derivative • diffeomorphism • Dimension • Eigenvalues and Eigenvectors • Einstein Field Equations • Einstein tensor • Equation • Error Term • estimation • existential quantification • Exterior (topology) • extreme curvature components • foliation • Fourier series • Gauge Theory • general covariance • general null frame transformations • General relativity • general theory of relativity • geodesic • Geodesics in general relativity • geometric analysis • Hawking mass • Hodge dual • hypersurface • I0 • Implicit function • Initial Condition • Initial value formulation (general relativity) • Initial Value Problem • Integration by parts • invariant quantities • Iteration • Iterative Method • Kerr metric • Lagrangian (field theory) • Lie derivative • linear differential equation • linear equation • Linearization • linear stability • Lorentz transformation • Lyapunov stability • Main effect • mathematical physics, differential geometry • Mathematics • Metric tensor (general relativity) • Minkowski space • Molecular orbital theory • Monotonic Function • Morawetz estimates • nonlinear system • Null hypersurface • null structure • Null vector • Orbital stability • Parameter • partial differential equation • Partial differential equations • Penrose diagram • Photon sphere • polarized symmetry • Pseudo-Riemannian manifold • pullback • Quantity • Reege-Wheeler equations • renormalization • Ricci coefficients • Ricci curvature • Riemann curvature tensor • scalar curvature • Schwarzschild coordinates • Schwarzschild metric • scientific notation • Second fundamental form • Simultaneous Equations • space form • Space-time • Special case • Stationary spacetime • Stress–energy tensor • Support (mathematics) • Symmetry group • Tangent Space • Tangent vector • Tensor • Theorem • Theorem M0 • Three-dimensional space (mathematics) • Topology • Transition function • Variable (mathematics) • Vector field • wave equation
• ISBN-10: 0-691-21852-8 / 0691218528
• ISBN-13: 978-0-691-21852-6 / 9780691218526