The Cauchy Problem for the Einstein Equations

Abstract

Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in this context. The question of producing reduced systems of equations which are hyperbolic is examined in detail and some new results on that subject are presented. Relevant background from the theory of partial differential equations is also explained at some length

98 pages

References in corpus (3)

• Einstein Constraints on Asymptotically Euclidean Manifolds
• A Scheme to Numerically Evolve Data for the Conformal Einstein Equation
• Well-posed forms of the 3+1 conformally-decomposed Einstein equations

Cited by in corpus (18)

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• Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI${}_0$
• Mathematical properties of cosmological models with accelerated expansion
• Global characteristic problem for the Einstein vacuum equations with small initial data, (II): The existence proof
• Mathematical general relativity: a sampler
• Global characteristic problem for Einstein vacuum equations with small initial data: (I) The initial data constraints
• On the Choquet-Bruhat-York-Friedrich formulation of the Einstein-Euler equations
• Relativistic Lagrange Formulation
• The existence of smooth solutions in q-theories
• Smoothness at null infinity and the structure of initial data
• Local existence in a class of characteristic problems for the Einstein vacuum equations
• The plane symmetric Einstein-dust system with positive cosmological constant
• Conformal Einstein evolution
• The Global Future Stability of the FLRW Solutions to the Dust-Einstein System with a Positive Cosmological Constant