Equivalence between the ADM-Hamiltonian and the harmonic coordinates approaches to the third postNewtonian dynamics of compact binaries - INSPIRE

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Equivalence between the ADM-Hamiltonian and the harmonic coordinates approaches to the third postNewtonian dynamics of compact binaries

Thibault Damour
(
- IHES, Bures-sur-Yvette
)
,
Piotr Jaranowski
(
- Warsaw U., Bialystok
)
,
Gerhard Schaefer
(
- Jena U.
)

Oct, 2000

13 pages

Published in:

Phys.Rev.D 63 (2001) 044021,
Phys.Rev.D 66 (2002) 029901 (erratum)

e-Print:

gr-qc/0010040 [gr-qc]

DOI:

View in:

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Abstract: (arXiv)

The third post-Newtonian approximation to the general relativistic dynamics of two point-mass systems has been recently derived by two independent groups, using different approaches, and different coordinate systems. By explicitly exhibiting the map between the variables used in the two approaches we prove their physical equivalence. Our map allows one to transfer all the known results of the Arnowitt-Deser-Misner (ADM) approach to the harmonic-coordinates one: in particular, it gives the value of the harmonic-coordinates Lagrangian, and the expression of the ten conserved quantities associated to global Poincar\'e invariance.

Note:

REVTeX, 13 pages, corrected misprint (wrong sign) in Eq. (4.7), updated references

References(24)

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- ERRATUM-IBID D66:029901 2002

Radiation Reaction and Angular Momentum Loss in Small Angle Gravitational Scattering

Thibault Damour
(
- Meudon Observ.
)
,
Nathalie Deruelle
(
- Poincare Inst.
)

- Phys.Lett.A 87 (1981) 81
•
DOI:
- 10.1016/0375-9601(81)90567-3

- Compt.Rend.Acad.Sci.Ser.II 294 1355

Lagrangians for $n$ point masses at the second post-Newtonian approximation of general relativity

Thibault Damour
(
- Meudon Observ. and
- Garching, Max Planck Inst.
)
,
Gerhard Schäfer
(
- Konstanz U.
)

- Gen.Rel.Grav. 17 (1985) 879-905
•
DOI:
- 10.1007/BF00773685

The Gravitational Quadrupole Radiation Reaction Force and the Canonical Formalism of Adm

Gerhard Schaefer
(
- Konstanz U.
)

- Annals Phys. 161 (1985) 81-100,
- Ann. Phys. ( N.y.) 161 ( 1985) 81-100
•
DOI:
- 10.1016/0003-4916(85)90337-9

The ADM Hamiltonian at the postlinear approximation

Gerhard Schäfer

- Gen.Rel.Grav. 18 (1986) 3, 255-270
•
DOI:
- 10.1007/bf00765886

- Astron.Lett. 29 516

Gravitational field and equations of motion of compact binaries to 5/2 postNewtonian order

- Phys.Rev.D 58 (1998) 124002
•
e-Print:
- gr-qc/9804079
•
DOI:
- 10.1103/PhysRevD.58.124002

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

Piotr Jaranowski
(
- Warsaw U., Bialystok
)
,
Gerhard Schaefer
(
- Jena U.
)

- Phys.Rev.D 57 (1998) 7274-7291,
- Phys.Rev.D 63 (2001) 029902 (erratum)
•
e-Print:
- gr-qc/9712075
•
DOI:
- 10.1103/PhysRevD.57.7274

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

Piotr Jaranowski
(
- Warsaw U., Bialystok
)
,
Gerhard Schaefer
(
- Jena U.
)

- Phys.Rev.D 57 (1998) 7274-7291,
- Phys.Rev.D 63 (2001) 029902 (erratum)
•
e-Print:
- gr-qc/9712075
•
DOI:
- 10.1103/PhysRevD.57.7274

The Binary black hole problem at the third postNewtonian approximation in the orbital motion: Static part

Piotr Jaranowski
(
- Warsaw U., Bialystok
)
,
Gerhard Schaefer
(
- Jena U.
)

- Phys.Rev.D 60 (1999) 124003
•
e-Print:
- gr-qc/9906092
•
DOI:
- 10.1103/PhysRevD.60.124003

Dynamical invariants for general relativistic two-body systems at the third postNewtonian approximation

Thibault Damour
(
- IHES, Bures-sur-Yvette
)
,
Piotr Jaranowski
(
- Warsaw U., Bialystok
)
,
Gerhard Schaefer
(
- Jena U.
)

- Phys.Rev.D 62 (2000) 044024
•
e-Print:
- gr-qc/9912092
•
DOI:
- 10.1103/PhysRevD.62.044024

Poincare invariance in the ADM Hamiltonian approach to the general relativistic two-body problem

Thibault Damour
(
- IHES, Bures-sur-Yvette
)
,
Piotr Jaranowski
(
- Warsaw U., Bialystok
)
,
Gerhard Schaefer
(
- Jena U.
)

- Phys.Rev.D 62 (2000) 021501,
- Phys.Rev.D 63 (2001) 029903 (erratum)
•
e-Print:
- gr-qc/0003051
•
DOI:
- 10.1103/PhysRevD.62.021501

Poincare invariance in the ADM Hamiltonian approach to the general relativistic two-body problem

Thibault Damour
(
- IHES, Bures-sur-Yvette
)
,
Piotr Jaranowski
(
- Warsaw U., Bialystok
)
,
Gerhard Schaefer
(
- Jena U.
)

- Phys.Rev.D 62 (2000) 021501,
- Phys.Rev.D 63 (2001) 029903 (erratum)
•
e-Print:
- gr-qc/0003051
•
DOI:
- 10.1103/PhysRevD.62.021501

Equations of motion of point particle binaries at the third postNewtonian order

Luc Blanchet
(
- Meudon Observ. and
- Potsdam, Max Planck Inst.
)
,
Guillaume Faye
(
- Meudon Observ.
)

- Phys.Lett.A 271 (2000) 58
•
e-Print:
- gr-qc/0004009
•
DOI:
- 10.1016/S0375-9601(00)00360-1

General relativistic dynamics of compact binaries at the third postNewtonian order

Luc Blanchet
(
- Meudon Observ.
)
,
Guillaume Faye
(
- Meudon Observ.
)

- Phys.Rev.D 63 (2001) 062005
•
e-Print:
- gr-qc/0007051
•
DOI:
- 10.1103/PhysRevD.63.062005

Radiative 3.5 postNewtonian ADM Hamiltonian for many body point - mass systems

Piotr Jaranowski
(
- Jena U.
)
,
Gerhard Schaefer
(
- Jena U.
)

- Phys.Rev.D 55 (1997) 4712-4722
•
DOI:
- 10.1103/PhysRevD.55.4712

- Annals Phys. 9 378

Hadamard regularization

Luc Blanchet
(
- Meudon Observ. and
- Caltech
)
,
Guillaume Faye
(
- Meudon Observ.
)

- J.Math.Phys. 41 (2000) 7675-7714
•
e-Print:
- gr-qc/0004008
•
DOI:
- 10.1063/1.1308506

Lorentzian regularization and the problem of point - like particles in general relativity

Luc Blanchet
(
- Meudon Observ. and
- Osaka U., Dept. Earth Space Sci.
)
,
Guillaume Faye
(
- Meudon Observ.
)

- J.Math.Phys. 42 (2001) 4391-4418
•
e-Print:
- gr-qc/0006100
•
DOI:
- 10.1063/1.1384864

On the determination of the last stable orbit for circular general relativistic binaries at the third postNewtonian approximation

Thibault Damour
(
- IHES, Bures-sur-Yvette
)
,
Piotr Jaranowski
(
- Warsaw U., Bialystok
)
,
Gerhard Schaefer
(
- Jena U.
)

- Phys.Rev.D 62 (2000) 084011
•
e-Print:
- gr-qc/0005034
•
DOI:
- 10.1103/PhysRevD.62.084011

Effective one-body approach to general relativistic two-body dynamics

A. Buonanno
(
- IHES, Bures-sur-Yvette
)
,
T. Damour
(
- IHES, Bures-sur-Yvette and
- Meudon Observ.
)

- Phys.Rev.D 59 (1999) 084006
•
e-Print:
- gr-qc/9811091
•
DOI:
- 10.1103/PhysRevD.59.084006

Transition from inspiral to plunge in binary black hole coalescences

Alessandra Buonanno
(
- Caltech and
- IHES, Bures-sur-Yvette
)
,
Thibault Damour
(
- IHES, Bures-sur-Yvette and
- DARC, Meudon
)

- Phys.Rev.D 62 (2000) 064015
•
e-Print:
- gr-qc/0001013
•
DOI:
- 10.1103/PhysRevD.62.064015

- Compt.Rend.Acad.Sci.Ser.II 293 537