The Second Post-Newtonian Equations of Hydrodynamics in General Relativity

Chandrasekhar, S.; Nutku, Y.

doi:10.1086/150171

Cited by 140 publications

(132 citation statements)

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“…11 The result (3.15) agrees with the non-local action for the 4PN tail term which has been considered in [67] [see Eq. (4.4) there] and investigated in the effective field theory approach [74,75].…”

Section: The Tail Effect At 4pn Ordersupporting

confidence: 78%

“…Historical works on the PN equations of motion of compact binaries include Lorentz & Droste [6], Einstein, Infeld & Hoffmann [7], Fock [8,9], Chandrasekhar and collaborators [10][11][12], as well as Otha et al [13][14][15]. These works culminated in the 1980s with the derivation of the equations of motion up to 2.5PN order, where radiation reaction effects appear [16][17][18] (see also [19][20][21][22][23][24] for alternative derivations), and led to the successful analysis of the time of arrival of the radio pulses from the Hulse-Taylor binary pulsar [25,26].…”

Section: Introductionmentioning

confidence: 99%

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Fokker action of nonspinning compact binaries at the fourth post-Newtonian approximation

et al. 2016

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The Fokker action governing the motion of compact binary systems without spins is derived in harmonic coordinates at the fourth post-Newtonian approximation (4PN) of general relativity.Dimensional regularization is used for treating the local UV divergences associated with point particles, followed by a renormalization of the poles into a redefinition of the trajectories of the point masses. Effects at the 4PN order associated with wave tails propagating at infinity are included consistently at the level of the action. A finite part procedure based on analytic continuation deals with the IR divergencies at spatial infinity, which are shown to be fully consistent with the presence of near zone tails. Our end result at 4PN order is Lorentz invariant and has the correct self-force limit for the energy of circular orbits. However, we find that it differs from the recently published result derived within the ADM Hamiltonian formulation of general relativity [T.Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 89, 064058 (2014)]. More work is needed to understand this discrepancy.

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Section: The Tail Effect At 4pn Ordersupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Fokker action of nonspinning compact binaries at the fourth post-Newtonian approximation

et al. 2016

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“…Clearly missing in this scheme is an explicit algorithm for the computation of h µν in the near zone. No such algorithm (say, in the spirit of the post-Minkowskian algorithm in Section 4) is known presently, but a lot is known on the first few post-Newtonian iterations [20,21,[44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]30,24]. The main difficulty in setting up a post-Newtonian algorithm is the appearance at some post-Newtonian order of divergent Poisson-like integrals.…”

Section: Post-newtonian Approximationmentioning

confidence: 99%

“…By expanding all powers of 1/c present into the matter densities (61) and into the retardations of the potentials (62), we find that the metric (63) becomes extremely complicated, as it really is (see e.g. [46,47,50,51]). Because of our use of retarded potentials, the metric (63) involves explicitly only even post-Newtonian terms (using the post-Newtonian terminology that even terms correspond to even powers of 1/c in the equations of motion).…”

Section: A the Inner Metric To 25pn Ordermentioning

confidence: 99%

Post-Newtonian Gravitational Radiation

Blanchet

1999

Einstein’s Field Equations and Their Physical Implications

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“…Refs. [10,11,12,13,14,15,16,17] for discussions). The method adopted in paper II to deal with these divergences has been to replace the Poisson integrals by a new type of solution to the hierarchy of post-Newtonian equations.…”

Section: Introductionmentioning

confidence: 99%

Structure of the post-Newtonian expansion in general relativity

2005

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In the continuation of a preceding work, we derive a new expression for the metric in the near zone of an isolated matter system in post-Newtonian approximations of general relativity. The post-Newtonian metric, a solution of the field equations in harmonic coordinates, is formally valid up to any order, and is cast in the form of a particular solution of the wave equation, plus a specific homogeneous solution which ensures the asymptotic matching to the multipolar expansion of the gravitational field in the exterior of the system. The new form is suitable for practical computations of the gravitational radiation reaction forces in harmonic coordinates. It also provides some insights on the structure of the post-Newtonian expansion in general relativity and the radiation reaction terms therein.

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The Second Post-Newtonian Equations of Hydrodynamics in General Relativity

Cited by 140 publications

References 0 publications

Fokker action of nonspinning compact binaries at the fourth post-Newtonian approximation

Fokker action of nonspinning compact binaries at the fourth post-Newtonian approximation

Post-Newtonian Gravitational Radiation

Structure of the post-Newtonian expansion in general relativity

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