Palatini Formalism of 5-Dimensional Kaluza-Klein Theory
arXiv:gr-qc/0503023 · doi:10.1142/S0217732305015689
Abstract
The Einstein field equations can be derived in $n$ dimensions ($n>2$) by the variations of the Palatini action. The Killing reduction of 5-dimensional Palatini action is studied on the assumption that pentads and Lorentz connections are preserved by the Killing vector field. A Palatini formalism of 4-dimensional action for gravity coupled to a vector field and a scalar field is obtained, which gives exactly the same fields equations in Kaluza-Klein theory.
10 pages