ADM canonical formalism for gravitating spinning objects

Abstract

In general relativity, systems of spinning classical particles are implemented into the canonical formalism of Arnowitt, Deser, and Misner [1]. The implementation is made with the aid of a symmetric stress-energy tensor and not a 4-dimensional covariant action functional. The formalism is valid to terms linear in the single spin variables and up to and including the next-to-leading order approximation in the gravitational spin-interaction part. The field-source terms for the spinning particles occurring in the Hamiltonian are obtained from their expressions in Minkowski space with canonical variables through 3-dimensional covariant generalizations as well as from a suitable shift of projections of the curved spacetime stress-energy tensor originally given within covariant spin supplementary conditions. The applied coordinate conditions are the generalized isotropic ones introduced by Arnowitt, Deser, and Misner. As applications, the Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling, recently obtained by Damour, Jaranowski, and Schaefer [2], is rederived and the derivation of the next-to-leading order gravitational spin(1)-spin(2) Hamiltonian, shown for the first time in [3], is presented.Comment: REVTeX4, 18 pages. v1: published version. v2: corrected misprints in (8.4) and (9.3), updated reference

Next-to-leading order gravitational spin(1)-spin(2) dynamics in Hamiltonian form

“…Recently in [2] it has been shown that the matter source parts of the energy and momentum constraint equations, respectively H M and H M i , are given in terms of canonical position, momentum, and spin variables in the form, to the post-Newtonian orders indicated,…”

“…The result is based on the ADM canonical formalism [1] for spinning classical objects recently derived by Steinhoff, Schäfer, and Hergt [2] which already has shown its power by the derivation of the Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling, lately obtained by Damour, Jaranowski, and Schäfer [3].…”

Mergers of black-hole binaries with aligned spins: Waveform characteristics

“…The initial momenta of the equalmass binaries, with the exception of X1 UU, were chosen by integrating the post-Newtonian equations of motion, as outlined in [22,23], with spin contributions to the Hamiltonian adapted from [24][25][26][27][28] (although we work in the ADM gauge, the results from harmonic gauge using effective-field theory [26] have been shown to be equivalent [29,30]), and the flux from [31]. For the X1 UU configuration, we used simpler quasicircular initial parameters with no initial ingoing radial momentum.…”

Erratum: Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling for two nonprecessing black holes with aligned spins [Phys. Rev. D87, 124036 (2013)]

“…[19]). This may be due simply to the fact that spin effects beyond the leading-order (LO) of the PN expansion series have been derived only in recent years [20][21][22][23][24][25][26][27][28][29][30][31][32], rather than to an intrinsic difficulty of the EOB approach to reproduce the spin interaction. Spin effects of coalescing BHBs have been included for the first time into the conservative part of the EOB formalism in Ref.…”