Canonical formulation of self-gravitating spinning-object systemsJan Steinhoff and Gerhard Schäfer
Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität - Max-Wien-Platz 1, 07743 Jena, Germany, EU
received 31 August 2009; accepted in final form 3 September 2009; published September 2009
published online 17 September 2009
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.
04.20.-q - Classical general relativity.
04.25.-g - Approximation methods; equations of motion.
97.80.-d - Binary and multiple stars.
© EPLA 2009