Next-to-leading order spin-orbit and spin(a)-spin(b) Hamiltonians for n gravitating spinning compact objects

Abstract

We derive the post-Newtonian next-to-leading order conservative spin-orbit and spin(a)-spin(b) gravitational interaction Hamiltonians for arbitrary many compact objects. The spin-orbit Hamiltonian completes the knowledge of Hamiltonians up to and including 2.5PN for the general relativistic three-body problem. The new Hamiltonians include highly nontrivial three-body interactions, in contrast to the leading order consisting of two-body interactions only. This may be important for the study of effects like Kozai resonances in mergers of black holes with binary black holes.

13 pages, 1 Mathematica source file, v2: submitted version, v3: published version, some minor corrections

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• Modelling gravitational waves from precessing black-hole binaries: Progress, challenges and prospects
• Aligned Spins: Orbital Elements, Decaying Orbits, and Last Stable Circular Orbit to high post-Newtonian Orders
• Elimination of the spin supplementary condition in the effective field theory approach to the post-Newtonian approximation
• Leading-order spin-orbit and spin(1)-spin(2) radiation-reaction Hamiltonians
• Stability and chaos of hierarchical three black hole configurations
• Canonical Angles In A Compact Binary Star System With Spinning Components: Approximative Solution Through Next-To-Leading-Order Spin-Orbit Interaction for Circular Orbits
• Eccentric Motion of Spinning Compact Binaries