Canonical formulation of self-gravitating spinning-object systems

2009/07/31 by Jan Steinhoff, Gerhard Schäfer · 6 citations
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #Pulsars and Gravitational Waves Research #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1209/0295-5075/87/50004

published as Europhys.Lett.87:50004,2009 · 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.

openalex publication_date 2009/09/01 · arxiv created 2010/04/19 · arxiv updated 2010/04/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

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 space-like hypersurfaces in standard ADM form. A new reduction of the tetrad degrees of freedom to the Einstein form of the metric field is suggested.

Cited by

• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin–orbit and leading order in spin(1)–spin(2) and spin-squared couplings
• Next-to-next-to-leading order post-Newtonian spin-orbit Hamiltonian for self-gravitating binaries
• New effective-one-body Hamiltonian with next-to-leading order spin-spin coupling
• Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order
• Highly relativistic spin-gravity coupling for fermions

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