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

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