Hyperbolicity of the 3+1 system of Einstein equations

DOI10.1007/BF01211832zbMath0521.53034OpenAlexW2042177590MaRDI QIDQ1055015

Yvonne Choquet-Bruhat, Tommaso Ruggeri

Publication date: 1983

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01211832

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Partial differential equations of mathematical physics and other areas of application (35Q99) Applications of local differential geometry to the sciences (53B50) Initial value problems for higher-order hyperbolic equations (35L30)

Related Items (21)

Well-posed constraint-preserving boundary conditions for the AA formulation of Einstein's equations ⋮ On the Newtonian limit of general relativity ⋮ Hyperbolic methods for Einstein's equations ⋮ Asymptotically Kasner-like singularities ⋮ Mathematical aspects of general relativity. Abstracts from the workshop held August 29 -- September 4, 2021 (hybrid meeting) ⋮ Cauchy's problem and Huygens' principle for the linearized Einstein field equations ⋮ CONSTRUCTING HYPERBOLIC SYSTEMS IN THE ASHTEKAR FORMULATION OF GENERAL RELATIVITY ⋮ PALATINI APPROACH TO MODIFIED GRAVITY: f(R) THEORIES AND BEYOND ⋮ Hyperbolic dynamics of discrete dynamical systems on pseudo-Riemannian manifolds ⋮ DIFFERENTIAL FORMS AND WAVE EQUATIONS FOR GENERAL RELATIVITY ⋮ The initial boundary value problem for the Einstein equations with totally geodesic timelike boundary ⋮ Numerical relativity as a tool for computational astrophysics ⋮ On sliced spaces: global hyperbolicity revisited ⋮ Hyperbolic evolution system for numerical relativity ⋮ Einstein and Yang-Mills Theories in Hyperbolic Form without Gauge Fixing ⋮ Hamiltonian Time Evolution for General Relativity ⋮ Fixing Einstein's Equations ⋮ Conformal “Thin-Sandwich” Data for the Initial-Value Problem of General Relativity ⋮ Well-posed forms of the 3+1 conformally-decomposed Einstein equations ⋮ Numerical relativity and compact binaries ⋮ Continuum and discrete initial-boundary value problems and Einstein's field equations

Cites Work

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• The Cauchy problem for the Yang-Mills equations
• Proiezioni naturali e derivazione trasversa in una varietà riemanniana a metrica iperbolica normale
• Propagateurs et commutateurs en relativité générale
• Republication of: The dynamics of general relativity
• The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. I. Local existence and smoothness properties
• Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
• Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires

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