Abstract
A class of spherically symmetric space-time metrics for which the scalar-field equation can be separated is systematically studied. Existence of normal modes is discussed by comparing the scalar product between radial solutions and induced by the field current, with that relative to the Weyl-Stone eigenvalue problem into which the separated radial equations can be put. It is found that the two scalar products are in general different. Conditions for their equivalence are determined. They contain particular results previously studied.
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