Following earlier work, it is inquired how far the 5-D Kaluza–Klein equations without sources may be reduced to the Einstein equations with sources. It is shown by algebraic means that this can be done, provided the extra part of the 5-D geometry is used appropriately to define an effective 4-D energy-momentum tensor. The latter has reasonable properties, but will require further detailed study.

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Some exact analytical solutions of the static Einstein–Maxwell equations for perfect and anisotropic fluids were found under the assumption of spherical symmetry and the existence of a one-parameter group of conformal motions. All solutions are matched to the Reissner‘xnNordström metric and possess positive energy density larger than the stresses, everywhere within the sphere.