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6
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84927491029
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A. Einstein, Über die Spezielle und die Allgemeine Relativitätstheorie (Vieweg, Braunschweig, 1920); English translation by R. W. Lawson, Relativity: The Special and the General Theory (Crown, New York, 1961).
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7
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84927468366
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D. Hilbert, 2 Mitt., Nachr. Ges. Wiss. Göttingen 53 (1917).
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18
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21144469215
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Our dust action is based on the canonical relativistic perfect fluid action discussed by
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(1993)
Class. Quantum Grav.
, vol.10
, pp. 1579
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Brown, J.D.1
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19
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0002436451
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This action makes use of a velocity potential or ``Clebsch'' representation of the fluid velocity [, ]. Clebsch potentials were used in the development of action principles for nonrelativistic fluids by Lin C. C. Lin, in Liquid Helium, edited by G. Careri (Academic, New York, 1963);
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(1859)
Angew. Math.
, vol.56
, pp. 1
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Clebsch, A.1
Reine, J.2
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20
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0002142650
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Variational Principles in Continuum Mechanics
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see also J. Serrin, in Handbuch der Physik, edited by S. Flügge and C. Truesdell (Springer, Berlin, 1959), Vol. 8 and by Seliger and Whitham [, ]. Tam used Clebsch potentials to formulate an action principle for an ideal, charged fluid in the context of special relativity [, 44, 2403, ]. Action principles for perfect fluids in general relativity were developed independently by Tam and O'Hanlon [, K. Tam, Can. J. Phys., K. Tam, J. O'Hanlon, Nuovo Cimento, 62B, 351, ] and by Schutz [, B. F. Schutz, Phys. Rev. D, 2, 2762, ]. The actions discussed by Tam and O'Hanlon and by Schutz use a minimal set of velocity potentials, which precludes the interpretation of the appropriate potential fields as Lagrangian coordinates for the fluid. The Hamiltonian form of Schutz's action was developed by Schutz [, B. F. Schutz, Angew. Math., ibid., 4, 3559, ] and by Demaret and Moncrief , J. Demaret, V. Moncrief, Phys. Rev. D, 21, 2785
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(1966)
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
, vol.305 A
, pp. 1
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Seliger, R.L.1
Whitham, G.B.2
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23
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84927481491
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K. V. Kuchař, in Directions in General Relativity, edited by B. L. Hu, M. P. Ryan, and C. V. Vishveshwara (Cambridge University Press, Cambridge, England, 1993), Vol. 1; J. D. Brown, in Proceedings of the Cornelius Lanczos Centenary Conference, edited by J. D. Brown, M. T. Chu, D. C. Ellison, and R. J. Plemmons (SIAM, Philadelphia, 1994).
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37
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84927495680
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Brown [17].
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38
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84927477091
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Schutz, first citation in Ref. [17].
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