Cauchy problems for the conformal vacuum field equations in general relativity

DOI10.1007/BF01206015zbMath0555.35116OpenAlexW1968740907MaRDI QIDQ760612

Helmut Friedrich

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1007/bf01206015

zbMATH Keywords

Cauchy problemsconformal hyperboloidal initial dataEinstein's conformal vacuum field equationsfirst order quasilinear symmetric hyperbolic systems

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Partial differential equations of mathematical physics and other areas of application (35Q99) Exact solutions to problems in general relativity and gravitational theory (83C15) Initial value problems for first-order hyperbolic systems (35L45)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The boost problem in general relativity
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Einstein's equations near spatial infinity
• A new definition of conformal and projective infinity of space-times
• The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system. I
• Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires
• Relativistic Kepler problem. I. Behavior in the distant past of orbits with gravitational radiation damping
• Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time
• Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system
• Characteristic initial data and wavefront singularities in general relativity
• An Approach to Gravitational Radiation by a Method of Spin Coefficients
• The scalar wave equation in a Schwarzschild space-time
• On the regular and the asymptotic characteristic initial value problem for Einstein’s vacuum field equations
• The asymptotic characteristic initial value problem for Einstein’s vacuum field equations as an initial value problem for a first-order quasilinear symmetric hyperbolic system
• On the existence of analytic null asymptotically flat solutions of Einstein’s vacuum field equations
• Zero rest-mass fields including gravitation: asymptotic behaviour
• The Large Scale Structure of Space-Time
• Symmetric hyperbolic linear differential equations

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