Generation of static solutions of a self-consistent system of Einstein-Klein-Gordon equations

A theorem is proved according to which a class of static solutions of a self-consistent system of Einstein-Klein-Gordon equations dependent on one arbitrary function is set in correspondence with a static solution of the Einstein equations with any given energy-momentum tensor T_ij. Two particular cases are examined as an illustration of this theorem. Methods of constructing the static solutions of a system of Einstein-Klein-Gordon equations with an ideal fluid energy-momentum tensor and a massive scalar field are indicated therein.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 11–14, June, 1989.