no. 3
A convergent post-newtonian approximation for the constraint equations in general relativity
Annales de l'I.H.P. Physique théorique, Tome 57 (1992) no. 3, pp. 279-317. 
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     author = {Lottermoser, M.},
     title = {A convergent post-newtonian approximation for the constraint equations in general relativity},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {279--317},
     publisher = {Gauthier-Villars},
     volume = {57},
     number = {3},
     year = {1992},
     mrnumber = {1185336},
     zbl = {0762.53053},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1992__57_3_279_0/}
}
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Lottermoser, M. A convergent post-newtonian approximation for the constraint equations in general relativity. Annales de l'I.H.P. Physique théorique, Tome 57 (1992) no. 3, pp. 279-317. http://www.numdam.org/item/AIHPA_1992__57_3_279_0/

[1] S. Chandrasekhar, The post-Newtonian equations of hydrodynamics in general relativity, Ap. J., Vol. 142, 1965, pp. 1488-1512. | MR

[2] A. Einstein, L. Infeld and B. Hoffmann, The gravitational equations and the problem of motion, Ann. Math., Vol. 39, 1938, pp. 65-100. | JFM | MR | Zbl

[3] J. Ehlers, Über den Newtonschen Grenzwert der Einsteinschen Gravitationstheorie, In J. NITSCH, J. PFARR and E.-W. STACHOW Eds., Grundlagenprobleme der modernen Physik, Mannheim, Wien, Zürich: Bibliographisches Institut, 1981, pp. 65-84. | MR

[4] J. Ehlers, On Limit Relations Between, And Approximative Explanations Of, Physical Theories, In R. BARCAN MARCUS, G. J. W. DORN and P. WEINGARTNER Eds., LogicMethodology and Philosophy of Science VII, , Amsterdam, etc., North Holland, 1986. (Studies in Logic and the Foundations of Mathematics; 114). pp. 387-403. | MR

[5] J.L. Anderson and T.C. Decanio, Equations of hydrodynamics in general relativity in the slow motion approximation Gen. Rel. Grav., Vol. 6, 1975, pp. 197-237. | Zbl

[6] G.D. Kerlick, Finite Reduced Hydrodynamic Equations in the Slow-Motion Approximation to General Relativity. Part II. Radiation Reaction and Higher-Order Divergent Terms, Gen. Rel. Grav., Vol. 12, 1980, pp. 521-543.

[7] J.L. Anderson, R.E. Kates, L.S. Kegeles and R.G. Madonna, Divergent integrals of post-Newtonian gravity: Nonanalytic terms in the near-zone expansion of a gravitationally radiating system found by matching, Phys. Rev. D, Vol. 25, 1982, pp. 2038-2048.

[8] L. Blanchet and T. Damour, Radiative Gravitational Fields in General Relativity. I. General Structure of the Field Outside the Source, Phil. Trans. R. Soc. Lond., Vol. A320, 1986, pp. 379-430. | MR | Zbl

[9] L. Blanchet and T. Damour, Tail-transported temporal correlations in the dynamics of a gravitating system; Phys. Rev. D., Vol. 37, 1988, pp. 1410-1435.

[10] T. Futamase and B.F. Schutz, The Newtonian and post-Newtonian approximations are asymptotic to general relativity, Phys. Rev. D., Vol. 28, 1983, pp. 2363-2372. | MR

[11] L.H. Loomis and S. Sternberg, Advanced Calculus, Reading/Mass., etc., Addison-Wesley, 1968. | MR | Zbl

[12] H. Cartan, Differential Calculus, Paris, Hermann/London, Kershaw, 1971. | MR

[13] C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, San Francisco, W. H. Freeman, 1973. | MR

[14] M. Cantor, Spaces of Functions with Asymptotic Conditions on Rn, Indiana Univ. Math. J., Vol. 24, (9), 1975, pp. 897-902. | MR | Zbl

[15] Y. Choquet-Bruhat and D. Christodoulou, Elliptic systems in Hs, δ spaces on manifolds which are Euclidean at infinity, Acta Math., Vol. 146, (1-2), 1981, pp. 129- 150. | MR | Zbl

[16] R.C. Mcowen, The Behavior of the Laplacian on Weighted Sobolev Spaces, Comm. Pure Appl. Math., Vol. 32, 1979, pp. 783-795. | MR | Zbl

[17] K. Deimling, Nonlinear Functional Analysis, Berlin, etc., Springer, 1985. | MR | Zbl

[18] V.A. Fock, Theory of Space, Time and Gravitation, London, New York, Pergamon Press, 1960. | Zbl

[19] J. Ehlers, Private communication, 1985.

[20] Y. Bruhat, The Cauchy Problem, in L. WITTEN Ed., Gravitation: an introduction to current research, New York, London, John Wiley and Sons, 1962, pp. 130-168. | MR

[21] Y. Choquet-Bruhat and J.W. York Jr., The Cauchy Problem, in A. HELD Ed., General Relativity and Gravitation, Vol. 1, New York, London, Plenum Press, 1980, pp. 99-172. | MR

[22] A. Chaljub-Simon and Y. Choquet-Bruhat, Global solutions of the Lichnerowicz equation in general relativity on an asymptotically Euclidean complete manifold, Gen. Rel. Grav., Vol. 12, (2), 1980, pp. 175-185. | MR | Zbl

[23] Y. Choquet-Bruhat, Recent Results on the Cauchy Problem in General Relativity, in Aspetti Matematici Della Teoria Della Relatività, Roma, Accademia Nazionale Dei Lincei, 1983, Atti Dei Convegni Lincei; 57, pp. 17-25.

[24] O. Reula, Private communication, June 1990.,

[25] J. Winicour, Newtonian gravity on the null cone, J. Math. Phys., Vol. 24, 1983, pp. 1193-1198. | MR | Zbl