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The Hamiltonian Structure of General Relativistic Perfect Fluids

Bao, David and Marsden, Jerrold and Walton, Ronald (1985) The Hamiltonian Structure of General Relativistic Perfect Fluids. Communications in Mathematical Physics, 99 (3). pp. 319-345. ISSN 0010-3616. doi:10.1007/BF01240351.

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We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift,, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed.

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Additional Information:© Springer-Verlag 1985. Received: 30 May 1984. SpringerLink Date: Wednesday, March 02, 2005. Communicated by S.-T. Yau. Research supported in part by NSF grant MCS 81-08814(A02). Research supported in part by NSF grant MCS 81-07086. Some initial discussions on this problem with Vince Moncrief were crucial to the success of our endeavors. We are greatly indebted to him. We also thank Judy Arms, Darryl Holm, Bob Jantzen, Richard Montgomery, Phil Morrison, Tudor Ratiu and Abe Taub for their interest and helpful comments.
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NSFMCS 81-08814(A02)
NSFMCS 81-07086
Issue or Number:3
Record Number:CaltechAUTHORS:20100713-074722902
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19009
Deposited By: Ruth Sustaita
Deposited On:13 Jul 2010 15:16
Last Modified:08 Nov 2021 23:48

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