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New theoretical techniques in the study of gravity

Fischer, Arthur E. and Marsden, Jerrold E. (1973) New theoretical techniques in the study of gravity. General Relativity and Gravitation, 4 (4). pp. 309-317. ISSN 0001-7701. doi:10.1007/BF00759850.

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Using new methods based on first order techniques, it is shown how sharp theorems for existence, uniqueness, and continuous dependence on the Cauchy data for the exterior Einstein equations can be proved simply and directly. Our main tools are obtained from the theory of quasilinear first order symmetric hyperbolic systems of partial differential equations. Einstein's equations in harmonic coordinates are cast into this form, thus achieving a certain uniformity of the description of gravity with other systems of partial differential equations occurring frequently in mathematical physics. In this symmetric hyperbolic form, the Cauchy problem for the exterior equations is easily resolved. Similarly, using first order techniques, a uniqueness theorem can be proved which increases by one the degree of differentiability of the coordinate-transformation between two solutions of Einstein's equations with the same Cauchy data. Finally it is shown how the theory of first order symmetric hyperbolic systems admits a global intrinsic treatment on manifolds.

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Additional Information:© 1973 Plenum Publishing Company Limited. Received 5 June 1972.
Issue or Number:4
Record Number:CaltechAUTHORS:20100806-073534073
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19306
Deposited By: Ruth Sustaita
Deposited On:06 Aug 2010 16:39
Last Modified:08 Nov 2021 23:51

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