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

By M. Levi, J. Steinhoff. 2015

179 citations recorded by the source corpus.

A bstractWe introduce a formulation for spinning gravitating objects in the effective field theory in the post-Newtonian scheme 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, and construct the spin-induced nonminimal couplings, where we obtain the leading order couplings to all orders in spin. We specify the 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 integrated out. The equations of motion of the spin can be directly obtained via a proper variation of the action, and Hamiltonians may be straightforwardly derived. 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. In particular, the proper next-to-leading order spin-squared potential and Hamiltonian for generic compact objects are also derived. 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. This formulation for spin is thus ideal for treatment of higher order spin dependent sectors.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/c85f95104541e42428e398c541d2a490be9939a8

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In Applied Mathematics

1. A. Luna
2. J. Vines
3. Ben Maybee
4. D. O’Connell
5. R. Roiban
6. J. Steinhoff

In Astronomy and Astrophysics

1. T. Damour
2. A. Luna
3. R. Roiban
4. D. O’Connell
5. Z. Bern
6. M. Zeng
7. Chia-Hsien Shen
8. J. Vines

Citations in the corpus

• Spinning black hole binary dynamics, scattering amplitudes, and effective field theory (2020, background): “Inclusion of spin effects in the post-Newtonian expansion has a long history in a variety of frameworks [51–57].”
• Observables and amplitudes for spinning particles and black holes (2019, methodology): “Meanwhile, calculating higher-order PN spin corrections has been a particular strength of the EFT treatment of PN dynamics [13, 28–33]; for reviews see [34, 35].”
• Dynamical Tides in General Relativity: Effective Action and Effective-One-Body Hamiltonian (2016, background): “Interestingly, the combination of boosts in the last term also appears in the computation of spin effects [86].”
• The simplest massive S-matrix: from minimal coupling to black holes (2018, unknown): “Next we consider the minimal spin coupling −12SμνΩ μν , given as [30, 33], − 2 SμνΩ μν = − 2 SABω AB μ u μ .”