Third post-Newtonian higher order ADM Hamilton dynamics for two-body point-mass systems

Abstract

The paper presents the conservative dynamics of two-body point-mass systems up to the third post-Newtonian order (1/c 6 ). The two-body dynamics is given in terms of a higher order ADM Hamilton function which results from a third post-Newtonian Routh functional for the total field-plus-matter system. The applied regularization procedures, together with making use of distributional differentiation of homogeneous functions, give unique results for the terms in the Hamilton function apart from the coefficient of the term (νp i ∂ i ) 2 r −1 . The result suggests an invalidation of the binary point-mass model at the third post-Newtonian order.PACS number(s): 04.

Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. II. Two-body equations of motion to second post-Newtonian order, and radiation reaction to 3.5 post-Newtonian order

“…Schäfer and Jaranowski [12][13][14] also derived 2PN, 2.5PN and 3.5PN contributions to the equations of motion in a Hamiltonian formulation. The 3PN contributions to the equations of motion have also been reported by several groups [15][16][17][18][19].…”

Sources of Gravitational Waves: Theory and Observations

“…The first important turning point was in 1993 when [44] pointed out the importance of computing the GW phasing beyond the leading order. Many crucial developments took place in the subsequent years [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. The second important turning point, which brought theory and observations closer, occurred in the mid and late 1990s when the construction of LIGO, Virgo, GEO600 and TAMA 300 detectors started [61].…”

“…This allowed the computation of spin-orbit and spin-spin couplings at quite high PN orders. So far, the ADM Hamiltonian approach has been developed mostly for the conservative dynamics through high PN orders [32,50,51,101,102,111,[120][121][122][123][124][125][126].…”

Dimensional regularization of the third post-Newtonian gravitational wave generation from two point masses

“…(1) The first step has been to compute all the terms, in both the 3PN equations of motion, either in Hamiltonian form [17,18,19,20] or using harmonic coordinates [21,22,23,24], and the 3.5PN gravitational radiation field, using a multipolar wave generation formalism [25,26,27,28], by means of the Hadamard self-field regularization [29,30,31,32], in short HR. (The 3.5PN terms in the equations of motion have been added in Refs.…”