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The Einstein Evolution Equations as a First-Order Quasi-Linear Symmetric Hyperbolic System, I

Fischer, Arthur E. and Marsden, Jerrold E. (1972) The Einstein Evolution Equations as a First-Order Quasi-Linear Symmetric Hyperbolic System, I. Communications in Mathematical Physics, 28 (1). pp. 1-38. ISSN 0010-3616. doi:10.1007/BF02099369.

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A systematic presentation of the quasi-linear first order symmetric hyperbolic systems of Friedrichs is presented. A number of sharp regularity and smoothness properties of the solutions are obtained. The present paper is devoted to the case of R n with suitable asymptotic conditions imposed. As an example, we apply this theory to give new proofs of the existence and uniqueness theorems for the Einstein equations in general relativity, due to Choquet-Bruhat and Lichnerowicz. These new proofs usingfirst order techniques are considerably simplier than the classical proofs based onsecond order techniques. Our existence results are as sharp as had been previously known, and our uniqueness results improve by one degree of differentiability those previously existing in the literature.

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Additional Information:© by Springer-Verlag 1972. Received January 25: in revised form May 4, 1972. Partially supported by AEC Contract AT(04-3)-34. Partially Supported by NSF Contract GP-8257. We thank H. Brezis. Y. Choquct-Bruhat. M. Cantor. D. Ebin. K. O. Friedrichs. T. Kato. H. Kiinzlc. P. Lux. H. Levy. A. Lichnerowicz. M. Protter. R. Sachs. and A. Taub for several helpful discussions.
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ID Code:19293
Deposited By: Ruth Sustaita
Deposited On:05 Aug 2010 18:43
Last Modified:08 Nov 2021 23:51

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