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Hamiltonian analysis of $n$-dimensional Palatini gravity with matter

Muxin Han·Yongge Ma·You Ding·Li Qin
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Abstract

We consider the Palatini formalism of gravity with cosmological constant $Λ$ coupled to a scalar field $ϕ$ in $n$-dimensions. The $n$-dimensional Einstein equations with $Λ$ can be derived by the variation of the coupled Palatini action provided $n>2$. The Hamiltonian analysis of the coupled action is carried out by a $1+(n-1)$ decomposition of the spacetime. It turns out that both Palatini action and Hilbert action lead to the same geometric dynamics in the presence of $Λ$ and $ϕ$. While, the $n$-dimensional Palatini action could not give a connection dynamics formalism directly.

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Muxin Han, Yongge Ma, You Ding, Li Qin. 2005-03-05. Hamiltonian analysis of $n$-dimensional Palatini gravity with matter. https://doi.org/10.1142/s0217732305017068

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