On the Field Equations of Kaluza's Theory

TL;DR

This paper analyzes Kaluza's original field equations, showing they modify Einstein's equations and can explain electrostatics within Schwarzschild geometry, suggesting a new interpretation of mass and charge effects.

Contribution

It demonstrates that Kaluza's theory leads to modified Einstein equations with an extra energy-momentum tensor, enabling Schwarzschild geometry to incorporate electrostatics.

Findings

Extra energy-momentum tensor modifies Einstein's equations.

Schwarzschild geometry can model electrostatics.

Deviation from Reissner-Nordstrom geometry explained.

Abstract

The field equations of the original Kaluza's theory are analyzed and it is shown that they lead to modification of Einstein's equations. The appearing extra energy-momentum tensor is studied and an example is given where this extra energy-momentum tensor is shown to allow four-dimensional Schwarzschild geometry to accommodate electrostatics. Such deviation from Reissner-Nordstrom geometry can account for the interpretation of Schwarzschild geometry as resulting not from mass only, but from the combined effects of mass and electric charge, even electric charge alone.