Palatini Formalism of 5-Dimensional Kaluza-Klein Theory

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.

arXiv comment10 pages

References in corpus (7)

• Background Independent Quantum Gravity: A Status Report
• Palatini form of 1/R gravity
• Palatini approach to Born-Infeld-Einstein theory and a geometric description of electrodynamics
• Application of the Campbell-Magaard theorem to higher-dimensional physics
• $R^2$ corrections to the cosmological dynamics of inflation in the Palatini formulation
• Palatini approach to 1/R gravity and its implications to the late Universe
• Killing Reduction of 5-Dimensional Spacetimes

Cited by in corpus (2)

• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Hamiltonian analysis of $n$-dimensional Palatini gravity with matter