Physically Acceptable Solution of Einstein's Equation for Many-Body System

Ohta, T.; Okamura, Hiroshi; Kimura, Toshiei; Hiida, Kichiro

doi:10.1143/ptp.50.492

Cited by 80 publications

(73 citation statements)

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“…12 This point has been suggested to us by T. Damour (private communication). 13 We present here the expression in 3 dimensions. Later we shall use dimensional regularization, so we shall need the easily generalized d-dimensional expression.…”

Section: Pn Iteration Of the Fokker Actionmentioning

confidence: 99%

“…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: Pn Iteration Of the Fokker Actionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2016

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“…Petrova [98], Fock [99] and Papapetrou [100] also obtained the equations of motion for the centres of extended bodies at 1PN order. Kimura, Ohta and collaborators introduced the ADM Hamiltonian formalism for doing PN computations [101,102] and started the computation of the equations of motion for nonspinning bodies at 2PN order [103,104]. The equations of motion for nonspinning point masses through 2.5PN order in harmonic coordinates were obtained by Damour and Deruelle [31,33], who built on the nonlinear iteration of the metric proposed by Bel et al [105].…”

Section: Direct Integration Of the Relaxed Einstein Equationsmentioning

confidence: 99%

Sources of Gravitational Waves: Theory and Observations

Buonanno

Sathyaprakash²

2015

General Relativity and Gravitation

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“…In the 1970s, Ohta et al [8,9,10] derived conditions for the post-Newtonian metric of an N-particle system in the transverse-traceless ADM (ADM-TT) gauge. The structure of this metric was given to 2.5 PN order by Schäfer [11]: Strain waveforms for an equal-mass, zero-spin binary of total mass M , from three initial separations r i (h f indicates the resolution of the highest-refinement region in the numerical simulation supplying each waveform).…”

Section: Post-newtonian Metric In the Adm-tt Gaugementioning

confidence: 99%

Post-Newtonian initial data with waves: progress in evolution

Kelly

Tichy

Zlochower

et al. 2010

Class. Quantum Grav.

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Abstract. In Kelly et al.[1], we presented new binary black-hole initial data adapted to puncture evolutions in numerical relativity. This data satisfies the constraint equations to 2.5 post-Newtonian order, and contains a transverse-traceless "wavy" metric contribution, violating the standard assumption of conformal flatness. We report on progress in evolving this data with a modern moving-puncture implementation of the BSSN equations in several numerical codes. We discuss the effect of the new metric terms on junk radiation and continuity of physical radiation extracted.

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Physically Acceptable Solution of Einstein's Equation for Many-Body System

Cited by 80 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

Sources of Gravitational Waves: Theory and Observations

Post-Newtonian initial data with waves: progress in evolution

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