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  Hamiltonian of a spinning test-particle in curved spacetime [Erratum: Phys. Rev. D 80, 104025 (2009)]

Barausse, E., Racine, E., & Buonanno, A. (2012). Hamiltonian of a spinning test-particle in curved spacetime [Erratum: Phys. Rev. D 80, 104025 (2009)]. Physical Review D, 85: 069904. doi:10.1103/PhysRevD.85.069904.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0015-8498-2 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0017-E7AD-0
Genre: Journal Article

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ErratumPhysRevD.85.pdf (Supplementary material), 29KB
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Barausse, Enrico, Author
Racine, Etienne, Author
Buonanno, Alessandra1, 2, Author              
Affiliations:
1Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:1933290              
2Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, escidoc:persistent22              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,Astrophysics, Cosmology and Extragalactic Astrophysics, astro-ph.CO,High Energy Physics - Theory, hep-th
 Abstract: Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test-particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase-space algebra in the Newton-Wigner spin supplementary condition (SSC), suitably generalized to curved spacetime, and find that the phase-space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in Post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner (ADM) canonical Hamiltonian computed in PN theory in the test-particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type S_Kerr S (and S_Kerr^2) through 3PN order, S_Kerr being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test-particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order.

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 Dates: 2009-07-272011-04-132012
 Publication Status: Published in print
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 Rev. Method: -
 Identifiers: arXiv: 0907.4745
DOI: 10.1103/PhysRevD.85.069904
URI: http://arxiv.org/abs/0907.4745
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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : American Physical Society
Pages: - Volume / Issue: 85 Sequence Number: 069904 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/111088197762258