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In the standard Einstein's theory the exterior gravitational field of anystatic and axially symmetric stellar object can be described by means of asingle function from which we obtain a metric into a four-dimensionalspace-time. In this work we present a generalization of those so called Weylsolutions to a space-time-matter metric in a five-dimensional manifold within anon-compactified Kaluza-Klein theory of gravity. The arising field equationsreduce to those of vacuum Einstein's gravity when the metric functionassociated to the fifth dimension is considered to be constant. The calculationof the geodesics allows to identify the existence or not of differentbehaviours of test particles, in orbits on a constant plane, between the twometrics. In addition, static solutions on the hypersurface orthogonal to theadded dimension but with time dependence in the five-dimensional metric arealso obtained. The consequences on the variation of the rest mass, if the fifthdimension is identified with it, are studied.

Gravitational fields of axially symmetric compact objects in 5D space-time-matter gravity