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Title: Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals

The next-to-next-to-leading order spin1-spin2 potential for an inspiralling binary, that is essential for accuracy to fourth post-Newtonian order, if both components in the binary are spinning rapidly, has been recently derived independently via the ADM Hamiltonian and the Effective Field Theory approaches, using different gauges and variables. Here we show the complete physical equivalence of the two results, thereby we first prove the equivalence of the ADM Hamiltonian and the Effective Field Theory approaches at next-to-next-to-leading order with the inclusion of spins. The main difficulty in the spinning sectors, which also prescribes the manner in which the comparison of the two results is tackled here, is the existence of redundant unphysical spin degrees of freedom, associated with the spin gauge choice of a point within the extended spinning object for its representative worldline. After gauge fixing and eliminating the unphysical degrees of freedom of the spin and its conjugate at the level of the action, we arrive at curved spacetime generalizations of the Newton-Wigner variables in closed form, which can also be used to obtain further Hamiltonians, based on an Effective Field Theory formulation and computation. Finally, we make use of our validated result to provide gauge invariant relations amongmore » the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to fourth post-Newtonian order, including all known sectors up to date.« less
Authors:
 [1] ;  [2]
  1. Institut d'Astrophysique de Paris, Université Pierre et Marie Curie, CNRS-UMR 7095, 98 bis Boulevard Arago, 75014 Paris (France)
  2. Centro Multidisciplinar de Astrofisica, Instituto Superior Tecnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)
Publication Date:
OSTI Identifier:
22382101
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2014; Journal Issue: 12; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCURACY; BINDING ENERGY; COUPLING; DEGREES OF FREEDOM; FIELD THEORIES; GAUGE INVARIANCE; HAMILTONIANS; POTENTIALS; SPACE-TIME; SPIN