Canonical formulation of self-gravitating spinning-object systems

TL;DR

This paper develops a canonical formulation for systems of classical spinning objects interacting through gravity, extending ADM formalism to include spin to linear order, with a fully reduced, constraint-free framework.

Contribution

It introduces a novel canonical formulation for self-gravitating spinning objects based on ADM, including a new tetrad reduction and a spatially symmetric gauge.

Findings

Variables satisfy standard Poisson brackets

Formulation is fully reduced without unresolved constraints

Proposes a new tetrad reduction to Einstein metric form

Abstract

Based on the Arnowitt-Deser-Misner (ADM) canonical formulation of general relativity, a canonical formulation of gravitationally interacting classical spinning-object systems is given to linear order in spin. The constructed position, linear momentum and spin variables fulfill standard Poisson bracket relations. A spatially symmetric time gauge for the tetrad field is introduced. The achieved formulation is of fully reduced form without unresolved constraints, supplementary, gauge, or coordinate conditions. The canonical field momentum is not related to the extrinsic curvature of spacelike hypersurfaces in standard ADM form. A new reduction of the tetrad degrees of freedom to the Einstein form of the metric field is suggested.