A sectorial approach to Kaluza-Klein theory
  The Kaluza and Klein versions of Kaluza-Klein theory are reviewed and compared. The differences in the field equations of the two theories are related to the transformation properties of the metrics employed. Based on this comparison a modified version of the Kaluza theory is proposed, in which the different sectors of the metric which describe gravitation, electromagnetism and the scalar field are considered to be partially separate entities, with distinct coordinate transformation properties. In addition, the cylinder condition is relaxed, so that it only affects the 4-D sector of the metric. This results in a theory in which the gravitational and electromagnetic fields are restricted to a four-dimensional brane, and the scalar field is restricted to the 5-D bulk. 
Terence V. Sewards