Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-07-27
Phys.Rev.D80:104025,2009; Erratum: Phys. Rev. D 85, 069904(E) (2012)
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Corrected typo in the ADM Hamiltonian at 3.5 PN order (eq. 6.20)
Scientific paper
10.1103/PhysRevD.80.104025
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.
Barausse Enrico
Buonanno Alessandra
Racine Étienne
No associations
LandOfFree
Hamiltonian of a spinning test-particle in curved spacetime does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Hamiltonian of a spinning test-particle in curved spacetime, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hamiltonian of a spinning test-particle in curved spacetime will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-246755