Palatini Formalism of 5-Dimensional Kaluza-Klein Theory

Details Palatini Formalism of 5-Dimensional Kaluza-Klein Theory Palatini Formalism of 5-Dimensional Kaluza-Klein Theory

2005-03-05

arxiv.org/abs/gr-qc/0503023v1

Mod.Phys.Lett. A20 (2005) 345-354

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages

Scientific paper

10.1142/S0217732305015689

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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