@article{AIHPA_1992__57_3_279_0, 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}, volume = {56}, year = {1992}, pages = {279-317}, mrnumber = {1185336}, zbl = {0762.53053}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPA_1992__57_3_279_0} }
Lottermoser, M. A convergent post-newtonian approximation for the constraint equations in general relativity. Annales de l'I.H.P. Physique théorique, Tome 56 (1992) pp. 279-317. http://gdmltest.u-ga.fr/item/AIHPA_1992__57_3_279_0/
[1] The post-Newtonian equations of hydrodynamics in general relativity, Ap. J., Vol. 142, 1965, pp. 1488-1512. | MR 191609
,[2] The gravitational equations and the problem of motion, Ann. Math., Vol. 39, 1938, pp. 65-100. | JFM 64.0769.01 | MR 1503389 | Zbl 0018.28103
, and ,[3] 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 653491
,[4] 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 874797
,[5] Equations of hydrodynamics in general relativity in the slow motion approximation Gen. Rel. Grav., Vol. 6, 1975, pp. 197-237. | Zbl 0379.76101
and ,[6] 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] 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.
, , and ,[8] 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 874095 | Zbl 0604.35073
and ,[9] Tail-transported temporal correlations in the dynamics of a gravitating system; Phys. Rev. D., Vol. 37, 1988, pp. 1410-1435.
and ,[10] The Newtonian and post-Newtonian approximations are asymptotic to general relativity, Phys. Rev. D., Vol. 28, 1983, pp. 2363-2372. | MR 726155
and ,[11] Advanced Calculus, Reading/Mass., etc., Addison-Wesley, 1968. | MR 227327 | Zbl 0162.35301
and ,[12] Differential Calculus, Paris, Hermann/London, Kershaw, 1971. | MR 344032
,[13] Gravitation, San Francisco, W. H. Freeman, 1973. | MR 418833
, and ,[14] Spaces of Functions with Asymptotic Conditions on Rn, Indiana Univ. Math. J., Vol. 24, (9), 1975, pp. 897-902. | MR 365621 | Zbl 0441.46028
,[15] Elliptic systems in Hs, δ spaces on manifolds which are Euclidean at infinity, Acta Math., Vol. 146, (1-2), 1981, pp. 129- 150. | MR 594629 | Zbl 0484.58028
and ,[16] The Behavior of the Laplacian on Weighted Sobolev Spaces, Comm. Pure Appl. Math., Vol. 32, 1979, pp. 783-795. | MR 539158 | Zbl 0426.35029
,[17] Nonlinear Functional Analysis, Berlin, etc., Springer, 1985. | MR 787404 | Zbl 0559.47040
,[18] Theory of Space, Time and Gravitation, London, New York, Pergamon Press, 1960. | Zbl 0085.42301
,[19] Private communication, 1985.
,[20] Gravitation: an introduction to current research, New York, London, John Wiley and Sons, 1962, pp. 130-168. | MR 143626
, The Cauchy Problem, in L. WITTEN Ed.,[21] The Cauchy Problem, in A. HELD Ed., General Relativity and Gravitation, Vol. 1, New York, London, Plenum Press, 1980, pp. 99-172. | MR 583716
and Jr.,[22] 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 575238 | Zbl 0443.35025
and ,[23] 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] Private communication, June 1990.,
,[25] Newtonian gravity on the null cone, J. Math. Phys., Vol. 24, 1983, pp. 1193-1198. | MR 702100 | Zbl 0522.76128
,