Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme - INSPIRE

DataBETA

Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme

Michele Levi
(
- Paris, Inst. Astrophys. and
- ILP, Paris
)
,
Jan Steinhoff
(
- Potsdam, Max Planck Inst. and
- Lisbon, IST
)

Jun 16, 2015

38 pages

Published in:

JCAP 01 (2016) 011

e-Print:

1506.05056 [gr-qc]

DOI:

10.1088/1475-7516/2016/01/011 (publication)

View in:

reference search96 citations

Citations per year

Abstract: (arXiv)

We implement the effective field theory for gravitating spinning objects in the post-Newtonian scheme at the next-to-next-to-leading order level to derive the gravitational spin-orbit interaction potential at the third and a half post-Newtonian order for rapidly rotating compact objects. From the next-to-next-to-leading order interaction potential, which we obtain here in a Lagrangian form for the first time, we derive straightforwardly the corresponding Hamiltonian. The spin-orbit sector constitutes the most elaborate spin dependent sector at each order, and accordingly we encounter a proliferation of the relevant Feynman diagrams, and a significant increase of the computational complexity. We present the evaluation of the interaction potential, going over contributing Feynman diagrams. The computation is carried out in terms of the nonrelativistic gravitational fields, together with the various gauge choices included in the effective field theory for gravitating spinning objects, which optimize the calculation. In addition, we automatize the effective field theory computations, and carry out the automated computations in parallel. Such automated effective field theory computations would be most useful to obtain higher order post-Newtonian corrections. We compare our Hamiltonian to the ADM Hamiltonian, and arrive at a complete agreement between the ADM and effective field theory results. We provide complete gauge invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to third and a half post-Newtonian order. The derivation presented here is essential to obtain further higher order post-Newtonian corrections, and to reach the accuracy level required for the successful detection of gravitational radiation.

Note:

38 pages, 6 figures; [v4] typos fixed eqs. (2.12),(2.34)

spin: dependence
gravitation: nonrelativistic
effective field theory
Hamiltonian
Feynman graph
higher-order
gravitational radiation
graviton
mathematical methods

References(41)

Figures(37)

[1]

LIGO webpage.

- http://www.ligo.caltech.edu

[2]

Virgo webpage.

- https://wwwcascina.virgo.infn.it

[3]

KAGRA webpage.

- http://gwcenter.icrr.u-tokyo.ac.jp/en

[4]

Post-Newtonian Theory for Gravitational Waves

Luc Blanchet
(
- Paris, Inst. Astrophys.
)

- Living Rev.Rel. 17 (2014) 2,
- Living Rev.Rel. 27 (2024) 1, 4
•
e-Print:
- 1310.1528
•
DOI:
- 10.12942/lrr-2014-2

[5]

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

[6]

Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems

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

- Phys.Rev.D 89 (2014) 6, 064058
•
e-Print:
- 1401.4548
•
DOI:
- 10.1103/PhysRevD.89.064058

[7]

Equations of motion of rotating bodies in general relativity theory / Errata. 18 after pg. 534

W. Tulczyjew

- Acta Phys.Polon. 18 (1959) 37-55

[8]

Probléme des deux corps et freinage de rayonnement en relativité générale, C. R. Acad / Sci. Paris Sér. II 294 1355-1357

T. Damour

[9]

Gravitational field and equations of motion of spinning compact binaries to 2.5 postNewtonian order

Hideyuki Tagoshi
(
- Osaka U.
)
,
Akira Ohashi
(
- Kyoto U., FIHS
)
,
Benjamin J. Owen
(
- Caltech and
- Potsdam, Max Planck Inst.
)

- Phys.Rev.D 63 (2001) 044006
•
e-Print:
- gr-qc/0010014
•
DOI:
- 10.1103/PhysRevD.63.044006

[10]

Higher-order spin effects in the dynamics of compact binaries. I. Equations of motion

Guillaume Faye
(
- Paris U. VI, GRECO and
- Paris, Inst. Astrophys.
)
,
Luc Blanchet
(
- Paris U. VI, GRECO and
- Paris, Inst. Astrophys.
)
,
Alessandra Buonanno
(
- Maryland U. and
- APC, Paris and
- Paris U. VI, GRECO and
- Paris, Inst. Astrophys.
)

- Phys.Rev.D 74 (2006) 104033
•
e-Print:
- gr-qc/0605139
•
DOI:
- 10.1103/PhysRevD.74.104033

[11]

Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling

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

- Phys.Rev.D 77 (2008) 064032
•
e-Print:
- 0711.1048
•
DOI:
- 10.1103/PhysRevD.77.064032

[12]

Next-to-next-to-leading order post-Newtonian spin-orbit Hamiltonian for self-gravitating binaries

Johannes Hartung
(
- Jena U.
)
,
Jan Steinhoff
(
- Jena U.
)

- Annalen Phys. 523 (2011) 783-790
•
e-Print:
- 1104.3079
•
DOI:
- 10.1002/andp.201100094

[13]

Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians

Johannes Hartung
(
- Jena U., TPI
)
,
Jan Steinhoff
(
- Jena U., TPI and
- Lisbon, IST and
- Lisbon, CENTRA
)
,
Gerhard Schafer
(
- Jena U., TPI
)

- Annalen Phys. 525 (2013) 359-394
•
e-Print:
- 1302.6723
•
DOI:
- 10.1002/andp.201200271

[14]

ADM canonical formalism for gravitating spinning objects

- Phys.Rev.D 77 (2008) 104018
•
e-Print:
- 0805.3136
•
DOI:
- 10.1103/PhysRevD.77.104018

[15]

Canonical formulation of self-gravitating spinning-object systems

Jan Steinhoff
(
- Jena U., TPI
)
,
Gerhard Schaefer
(
- Jena U., TPI
)

- EPL 87 (2009) 5, 50004
•
e-Print:
- 0907.1967
•
DOI:
- 10.1209/0295-5075/87/50004

[16]

Next-to-next-to-leading order spin-orbit effects in the equations of motion of compact binary systems

Sylvain Marsat
(
- Paris, Inst. Astrophys.
)
,
Alejandro Bohe
(
- Paris, Inst. Astrophys. and
- Balearic Islands U.
)
,
Guillaume Faye
(
- Paris, Inst. Astrophys.
)
,
Luc Blanchet
(
- Paris, Inst. Astrophys.
)

- Class.Quant.Grav. 30 (2013) 055007
•
e-Print:
- 1210.4143
•
DOI:
- 10.1088/0264-9381/30/5/055007

[17]

Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binaries

Alejandro Bohe
(
- Balearic Islands U.
)
,
Sylvain Marsat
(
- Paris U. VI, GRECO
)
,
Guillaume Faye
(
- Paris U. VI, GRECO
)
,
Luc Blanchet
(
- Paris U. VI, GRECO
)

- Class.Quant.Grav. 30 (2013) 075017
•
e-Print:
- 1212.5520
•
DOI:
- 10.1088/0264-9381/30/7/075017

[18]

Spinning gravitating objects in the effective field theory in the post-Newtonian scheme

Michele Levi
(
- ILP, Paris and
- Paris, Inst. Astrophys.
)
,
Jan Steinhoff
(
- Potsdam, Max Planck Inst. and
- Lisbon, IST
)

- JHEP 09 (2015) 219
•
e-Print:
- 1501.04956
•
DOI:
- 10.1007/JHEP09(2015)219

[19]

Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order

Michele Levi
(
- Hebrew U.
)

- Phys.Rev.D 85 (2012) 064043
•
e-Print:
- 1107.4322
•
DOI:
- 10.1103/PhysRevD.85.064043

[20]

An Effective field theory of gravity for extended objects

Walter D. Goldberger
(
- Yale U.
)
,
Ira Z. Rothstein
(
- Carnegie Mellon U.
)

- Phys.Rev.D 73 (2006) 104029
•
e-Print:
- hep-th/0409156
•
DOI:
- 10.1103/PhysRevD.73.104029

[21]

Les Houches lectures on effective field theories and gravitational radiation

Walter D. Goldberger
(
- Yale U.
)

e-Print:
- hep-ph/0701129

[22]

The Relativistic Spherical Top

- Annals Phys. 87 (1974) 498
•
DOI:
- 10.1016/0003-4916(74)90046-3

[23]

Lagrangian Dynamics of Spinning Particles and Polarized Media in General Relativity

I. Bailey
(
- Alberta U.
)
,
W. Israel
(
- Alberta U.
)

- Commun.Math.Phys. 42 (1975) 65-82
•
DOI:
- 10.1007/BF01609434

[24]

Post-Newtonian corrections to the motion of spinning bodies in NRGR

Rafael A. Porto
(
- Carnegie Mellon U.
)

- Phys.Rev.D 73 (2006) 104031
•
e-Print:
- gr-qc/0511061
•
DOI:
- 10.1103/PhysRevD.73.104031

[25]

Equations of motion for spinning particles in external electromagnetic and gravitational fields

Karl Yee
(
- UC, Irvine
)
,
Myron Bander
(
- UC, Irvine
)

- Phys.Rev.D 48 (1993) 2797-2799
•
e-Print:
- hep-th/9302117
•
DOI:
- 10.1103/PhysRevD.48.2797

1-25 of 41
1
2
25 / page