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Palatini Formalism of 5-Dimensional Kaluza-Klein Theory

You Ding·Yongge Ma·Muxin Han·Jianbing Shao
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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.

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You Ding, Yongge Ma, Muxin Han, Jianbing Shao. 2005-03-05. Palatini Formalism of 5-Dimensional Kaluza-Klein Theory. https://doi.org/10.1142/s0217732305015689

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