Canonical formulation of self-gravitating spinning-object systems

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.

6 pages. v2: extended version; identical to the published one. v3: corrected misprints in (24) and (39); improved notation; added note regarding a further reference.

References in corpus (4)

• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• ADM canonical formalism for gravitating spinning objects

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