The spacetime manifold is extended to a Weyl integrable spacetime (WIST). It is shown that this structure is a natural way to geometrize a long-range scalar field in the theory of gravitation. Several configurations are described in WIST (vacuum, dust, electromagnetic and external scalar field distribution). The general mechanism for studying all these cases and a special description of the analysis of the perfect fluid case are given.
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Salim et al. (1996) studied this question.
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