The Cauchy problem for Lorentz metrics with prescribed Ricci curvature
Compositio Mathematica, Volume 48 (1983) no. 3, p. 327-349
@article{CM_1983__48_3_327_0,
     author = {DeTurck, Dennis},
     title = {The Cauchy problem for Lorentz metrics with prescribed Ricci curvature},
     journal = {Compositio Mathematica},
     publisher = {Martinus Nijhoff Publishers},
     volume = {48},
     number = {3},
     year = {1983},
     pages = {327-349},
     zbl = {0527.53037},
     mrnumber = {700744},
     language = {en},
     url = {http://www.numdam.org/item/CM_1983__48_3_327_0}
}
DeTurck, Dennis M. The Cauchy problem for Lorentz metrics with prescribed Ricci curvature. Compositio Mathematica, Volume 48 (1983) no. 3, pp. 327-349. http://www.numdam.org/item/CM_1983__48_3_327_0/

[1] Y. Foures-Bruhat: "Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires", Acta. Math., 88 (1952) 141-225. | MR 53338 | Zbl 0049.19201

[2] Y. Choquet-Bruhat: "Cauchy problem", in Gravitation: an Introduction to Current Research, ed. L. Witten, Wiley, 1962. | MR 143626 | Zbl 0115.43103

[3] Y. Choquet-Bruhat and R. Geroch: "Global aspects of the Cauchy problem in general relativity", Comm. Math. Phys., 14 (1969) 329-335. | MR 250640 | Zbl 0182.59901

[4] D. Deturck: "Metrics with prescribed Ricci curvature", Seminar in Differential Geometry, ed S.T. Yau, Annals of Math. Study 102. | Zbl 0478.53031

[5] D. Deturck: "Existence of metrics with prescribed Ricci curvature: local theory", Inventiones Math. 65 (1981) 179-207. | MR 636886 | Zbl 0489.53014

[6] D. Deturck and J. Kazdan: "Some regularity theorems in Riemannian geometry", Ann. Scient. Ec. Norm. Sup. 4e ser., 14 (1981) 249-260. | Numdam | MR 644518 | Zbl 0486.53014

[7] A. Fischer and J. Marsden: "The Einstein evolution equation as a first-order, quasilinear symmetric hyperbolic system, I", Comm. Math. Phys., 28 (1972) 1-38. | MR 309507 | Zbl 0247.35082

[8] A. Fischer and J. Marsden: "The initial-value problem and the dynamical formulation of general relativity", in General Relativity, an Einstein Centenary Survey, ed. S. Hawking and W. Israel, Cambridge U. Press, 1979, pp. 138-211.

[9] R. Geroch: "General Relativity", Proc. Symp. Pure Math., vol. XXVII (2) (Differential Geometry), AMS, 1975, pp. 401-414. | MR 378703 | Zbl 0307.53038

[10] S. Hawking and G. Ellis: The large-scale structure of space-time, Cambridge U. Press, 1973. | MR 424186 | Zbl 0265.53054

[11] T. Hughes, T. Kato and J. Marsden: "Well-posed quasilinear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity", Arch. Rat. Mech. Anal., 63 (1977) 273-294. | MR 420024 | Zbl 0361.35046

[12] J. Kazdan: "Another proof of Bianchi's identity in Riemannian geometry", Proc. AMS, 81 (1981) 341-342. | MR 593487 | Zbl 0459.53033

[13] J. Leray: Hyperbolic Differential Equations, lecture notes, IAS, 1951-52.

[14] A. Lichnerowicz: "Propogateurs et commutateurs en relativité générale", Pub. Math. no. 10, I.H.E.S. Paris, 1961, pp. 293-344. | Numdam | MR 157736 | Zbl 0098.42607

[15] A. Lichnerowicz: Relativistic Magnetohydrodynamics, Benjamin, 1967. | Zbl 0193.55401

[16] C. Lanczos: "Ein vereinfachendes Koordinatensystem für die Einsteinschen Gravitationsgleichungen", Phys. Z. 23 (1922) 537-539. | JFM 48.1023.01

[17] L. Smarr: "Space-times generated by computers: Black holes with gravitational radiation", Proc. Eighth Texas Symp. on Relativistic Astrophysics, Ann. NY. Acad. Sci. 302 (1977) 569-604.

[18] J. Synge: Relativity: The General Theory, North-Holland, 1960. | MR 118457 | Zbl 0090.18504