Cauchy problem for the Einstein equations. III

The equations of small perturbations of the metric in synchronous coordinates are equivalent to a first-order system for which the Cauchy problem is correct only upon the satisfaction of several conditions imposed on the lowest symbols of the operator.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 105–109, November, 1982.