Linking the ADM formulation to other Hamiltonian formulations of general relativity

Abstract

We obtain the Arnowitt-Deser-Misner formulation of general relativity in $n$ dimensions ($n\ge 3$) from its either $SO(n-1,1)$ [$SO(n)$] or $SO(n-1)$ Palatini Hamiltonian formulations and vice versa [we recall that $SO(n-1,1)$ [$SO(n)$] requires no gauge fixing whereas $SO(n-1)$ involves the time gauge]. Similarly, the Hamiltonian formulation of general relativity in terms of Ashtekar-Barbero variables can also be directly obtained from the Arnowitt-Deser-Misner Hamiltonian formulation and vice versa, which is an alternative approach to the way followed by Barbero. We give the relevant maps among the phase-space variables and relate the corresponding symplectic structures and the first-class constraints.

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References in corpus (3)

• Manifestly Lorentz-covariant variables for the phase space of general relativity
• Canonical analysis of $n$-dimensional Palatini action without second-class constraints
• Revisiting the solution of the second-class constraints of the Holst action