Abstract
A class of metrics providing the complete separation of variables in the Klein-Gordon equation is considered. The general exact solution to the vacuum Einstein equation for such metrics is obtained by the variable separation method. It is shown that all these solutions correspond to curvilinear coordinate systems in the Minkowskian space-time. Several limit cases of such systems are investigated. Moreover, some other separating systems are constructed and it is shown that they make it possible to obtain partial exact solutions to nonlinear scalar field equations.
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