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Journal Article

Spinning gravitating objects in the effective field theory in the post-Newtonian scheme


Steinhoff,  Jan
Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Levi, M., & Steinhoff, J. (2015). Spinning gravitating objects in the effective field theory in the post-Newtonian scheme. Journal of High Energy Physics, 2015(09): 219. doi:10.1007/JHEP09(2015)219.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0025-039A-1
An effective field theory for gravitating spinning objects in the post-Newtonian approximation is formulated in the context of the binary inspiral problem. We aim at an effective action, where all field modes below the orbital scale are integrated out. We spell out the relevant degrees of freedom, in particular the rotational ones, and the associated symmetries. Building on these symmetries, we introduce the minimal coupling part of the point particle action in terms of gauge rotational variables. We then proceed to construct the spin-induced nonminimal couplings, where we obtain the leading order couplings to all orders in spin for the first time. We specify to a gauge for the rotational variables, where the unphysical degrees of freedom are eliminated already from the Feynman rules, and all the orbital field modes are conveniently integrated out. The equations of motion of spin are then directly obtained via a proper variation of the action, and they take on a simple form. We implement this effective field theory for spin to derive all spin dependent potentials up to next-to-leading order to quadratic level in spin, namely up to the third post-Newtonian order for rapidly rotating compact objects. For the implementations we use the nonrelativistic gravitational field decomposition, which is found here to eliminate higher-loop Feynman diagrams also in spin dependent sectors, and facilitates derivations. Finally, the corresponding Hamiltonians are also straightforwardly obtained from the potentials derived via this formulation. Thus, the formulation is ideal for the treatment of further higher order spin dependent sectors.