Kaluza–Klein equations, Einstein’s equations, and an effective energy-momentum tensor

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.