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Tail effect in gravitational radiation reaction: Time nonlocality and renormalization group evolution

Chad R. Galley1, Adam K. Leibovich2, Rafael A. Porto3, and Andreas Ross4

  • 1Theoretical Astrophysics (TAPIR), Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
  • 2Pittsburgh Particle Physics Astrophysics and Cosmology Center (PITT PACC), Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
  • 3ICTP South American Institute for Fundamental Research, Instituto de Física Teórica—Universidade Estadual Paulista Rua Dr. Bento Teobaldo Ferraz 271, 01140-070 São Paulo, São Paulo, Brazil
  • 4Department of Physics and Astronomy Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

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Phys. Rev. D 93, 124010 – Published 6 June, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.124010

Abstract

We use the effective field theory (EFT) framework to calculate the tail effect in gravitational radiation reaction, which enters at the fourth post-Newtonian order in the dynamics of a binary system. The computation entails a subtle interplay between the near (or potential) and far (or radiation) zones. In particular, we find that the tail contribution to the effective action is nonlocal in time and features both a dissipative and a “conservative” term. The latter includes a logarithmic ultraviolet (UV) divergence, which we show cancels against an infrared (IR) singularity found in the (conservative) near zone. The origin of this behavior in the long-distance EFT is due to the point-particle limit—shrinking the binary to a point—which transforms a would-be infrared singularity into an ultraviolet divergence. This is a common occurrence in an EFT approach, which furthermore allows us to use renormalization group (RG) techniques to resum the resulting logarithmic contributions. We then derive the RG evolution for the binding potential and total mass/energy, and find agreement with the results obtained imposing the conservation of the (pseudo) stress-energy tensor in the radiation theory. While the calculation of the leading tail contribution to the effective action involves only one diagram, five are needed for the one-point function. This suggests logarithmic corrections may be easier to incorporate in this fashion. We conclude with a few remarks on the nature of these IR/UV singularities, the (lack of) ambiguities recently discussed in the literature, and the completeness of the analytic post-Newtonian framework.

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References (82)

  1. W. D. Goldberger and I. Z. Rothstein, An Effective field theory of gravity for extended objects, Phys. Rev. D 73, 104029 (2006).
  2. J. B. Gilmore and A. Ross, Effective field theory calculation of second post-Newtonian binary dynamics, Phys. Rev. D 78, 124021 (2008).
  3. S. Foffa and R. Sturani, Effective field theory calculation of conservative binary dynamics at third post-Newtonian order, Phys. Rev. D 84, 044031 (2011).
  4. L. Blanchet, T. Damour, G. Esposito-Farese, and B. R. Iyer, Gravitational Radiation from Inspiralling Compact Binaries Completed at the Third post-Newtonian Order, Phys. Rev. Lett. 93, 091101 (2004).
  5. T. Damour, P. Jaranowski, and G. Schaefer, Equivalence between the ADM-Hamiltonian and the harmonic coordinates approaches to the third post-Newtonian dynamics of compact binaries, Phys. Rev. D 63, 044021 (2001); 66, 029901(E) (2002).
  6. Y. Itoh and T. Futamase, New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity, Phys. Rev. D 68, 121501 (2003).
  7. L. Blanchet, Gravitational radiation from Post-Newtonian sources and inspiralling compact binaries, Living Rev. Relativity 17, 2 (2014).
  8. W. D. Goldberger and A. Ross, Gravitational radiative corrections from effective field theory, Phys. Rev. D 81, 124015 (2010).
  9. A. Ross (unpublished).
  10. R. A. Porto, Post-Newtonian corrections to the motion of spinning bodies in NRGR, Phys. Rev. D 73, 104031 (2006).
  11. R. A. Porto and I. Z. Rothstein, The Hyperfine Einstein-Infeld-Hoffmann potential, Phys. Rev. Lett. 97, 021101 (2006).
  12. R. A. Porto and I. Z. Rothstein, Comment on “On the next-to-leading order gravitational spin(1)- spin(2) dynamics” by J. Steinhoff et al., arXiv:0712.2032.
  13. R. A. Porto and I. Z. Rothstein, Spin(1)-spin(2) effects in the motion of inspiralling compact binaries at third order in the post-Newtonian expansion, Phys. Rev. D 78, 044012 (2008).
  14. R. A. Porto and I. Z. Rothstein, Next to leading order spin(1)-spin(1) effects in the motion of inspiralling compact binaries, Phys. Rev. D 78, 044013 (2008).
  15. R. A. Porto, Next to leading order spin-orbit effects in the motion of inspiralling compact binaries, Classical Quantum Gravity 27, 205001 (2010).
  16. R. A. Porto, A. Ross, and I. Z. Rothstein, Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order, J. Cosmol. Astropart. Phys. 03 (2011) 009.
  17. R. A. Porto, A. Ross, and I. Z. Rothstein, Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order, J. Cosmol. Astropart. Phys. 09 (2012) 028.
  18. M. Levi, Next to leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction, Phys. Rev. D 82, 064029 (2010).
  19. D. L. Perrodin, Subleading spin-orbit cCorrection to the Newtonian potential in effective field theory formalism, in On recent developments in theoretical and experimental general relativity, astrophysics and relativistic field theories. Proceedings, 12th Marcel Grossmann Meeting on General Relativity, Paris, France, 2009. Vol. 1-3, p. 725 (2010), arXiv:1005.0634.
  20. M. Levi, Next to leading order gravitational spin-orbit coupling in an effective field theory approach, Phys. Rev. D 82, 104004 (2010).
  21. H. Tagohi, A. Ohashi, and B. J. Owen, Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order, Phys. Rev. D 63, 044006 (2001).
  22. G. Faye, L. Blanchet, and A. Buonanno, Higher-order spin effects in the dynamics of compact binaries. I. Equations of motion, Phys. Rev. D 74, 104033 (2006).
  23. L. Blanchet, A. Buonanno, and G. Faye, Higher-order spin effects in the dynamics of compact binaries. II. Radiation field, Phys. Rev. D 74, 104034 (2006); 81, 089901(E) (2010).
  24. T. Damour, P. Jaranowski, and G. Schaefer, Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling, Phys. Rev. D 77, 064032 (2008).
  25. J. Steinhoff, S. Hergt, and G. Schaefer, On the next-to-leading order gravitational spin(1)-spin(2) dynamics, Phys. Rev. D 77, 081501 (2008).
  26. J. Steinhoff, S. Hergt, and G. Schaefer, Spin-squared Hamiltonian of next-to-leading order gravitational interaction, Phys. Rev. D 78, 101503 (2008).
  27. S. Hergt, J. Steinhoff, and G. Schaefer, On the comparison of results regarding the post-Newtonian approximate treatment of the dynamics of extended spinning compact binaries, J. Phys. Conf. Ser. 484, 012018 (2014).
  28. S. Hergt, J. Steinhoff, and G. Schaefer, Reduced Hamiltonian for next-to-leading order spin-squared dynamics of general compact binaries, Classical Quantum Gravity 27, 135007 (2010).
  29. A. Bohe, G. Faye, S. Marsat, and E. K. Porter, Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order, arXiv:1501.01529.
  30. A. Ross, Multipole expansion at the level of the action, Phys. Rev. D 85, 125033 (2012).
  31. A. Buonanno, G. Faye, and T. Hinderer, Spin effects on gravitational waves from inspiraling compact binaries at second post-Newtonian order, Phys. Rev. D 87, 044009 (2013).
  32. M. Levi, Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order, Phys. Rev. D 85, 064043 (2012).
  33. M. Levi and J. Steinhoff, Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme, J. Cosmol. Astropart. Phys. 01 (2016) 011.
  34. M. Levi and J. Steinhoff, Next-to-next-to-leading order gravitational spin-squared potential via the effective field theory for spinning objects in the post-Newtonian scheme, J. Cosmol. Astropart. Phys. 01 (2016) 008.
  35. M. Levi and J. Steinhoff, Equivalence of ADM Hamiltonian and effective field theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals, J. Cosmol. Astropart. Phys. 12 (2014) 003.
  36. J. Hartung, J. Steinhoff, and G. Schaefer, Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians, Ann. Phys. (Berlin) 525, 359 (2013).
  37. S. Marsat, A. Bohe, G. Faye, and L. Blanchet, Next-to-next-to-leading order spin-orbit effects in the equations of motion of compact binary systems, Classical Quantum Gravity 30, 055007 (2013).
  38. J. Hartung and J. Steinhoff, Next-to-next-to-leading order post-Newtonian spin(1)-spin(2) Hamiltonian for self-gravitating binaries, Ann. Phys. (Berlin) 523, 919 (2011).
  39. V. Vaidya, Gravitational spin Hamiltonians from the S matrix, Phys. Rev. D 91, 024017 (2015).
  40. M. Levi and J. Steinhoff, Leading order finite size effects with spins for inspiralling compact binaries, J. High Energy Phys. 06 (2015) 059.
  41. S. Marsat, Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries, Classical Quantum Gravity 32, 085008 (2015).
  42. A. Buonanno and B. S. Sathyaprakash, Sources of Gravitational Waves: Theory and Observations, arXiv:1410.7832.
  43. A. Le Tiec, The overlap of numerical relativity, perturbation theory and post-Newtonian theory in the binary black hole problem, Int. J. Mod. Phys. D 23, 1430022 (2014).
  44. W. D. Goldberger, Les Houches lectures on effective field theories and gravitational radiation, in Les Houches Summer School—Session 86: Particle Physics and Cosmology: The Fabric of Spacetime Les Houches, France, 2006. 2007, arXiv:hep-ph/0701129.
  45. S. Foffa and R. Sturani, Effective field theory methods to model compact binaries, Classical Quantum Gravity 31, 043001 (2014).
  46. R. A. Porto, The Effective Field Theorist’s Approach to Gravitational Dynamics, arXiv:1601.04914.
  47. C. R. Galley, Effective Field Theory and Gravity (to be published).
  48. P. Jaranowski and G. Schaefer, Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems, Phys. Rev. D 86, 061503 (2012).
  49. P. Jaranowski and G. Schfer, Dimensional regularization of local singularities in the 4th post-Newtonian two-point-mass Hamiltonian, Phys. Rev. D 87, 081503 (2013).
  50. P. Jaranowski and G. Schaefer, Derivation of the local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries, Phys. Rev. D 92, 124043 (2015).
  51. T. Damour, P. Jaranowski, and G. Schaefer, Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems, Phys. Rev. D 89, 064058 (2014).
  52. L. Bernard, L. Blanchet, A. Boh, G. Faye, and S. Marsat, Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation, Phys. Rev. D 93, 084037 (2016).
  53. S. Foffa and R. Sturani, Dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant, Phys. Rev. D 87, 064011 (2013).
  54. T. Damour, P. Jaranowski, and G. Schfer, On the conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity, Phys. Rev. D 93, 084014 (2016).
  55. L. Blanchet, Time asymmetric structure of gravitational radiation, Phys. Rev. D 47, 4392 (1993).
  56. W. D. Goldberger, A. Ross, and I. Z. Rothstein, Black hole mass dynamics and renormalization group evolution, Phys. Rev. D 89, 124033 (2014).
  57. L. Blanchet, S. L. Detweiler, A. Le Tiec, and B. F. Whiting, High-order post-Newtonian fit of the gravitational self-force for circular orbits in the Schwarzschild geometry, Phys. Rev. D 81, 084033 (2010).
  58. C. R. Galley and B. Hu, Self-force on extreme mass ratio inspirals via curved spacetime effective field theory, Phys. Rev. D 79, 064002 (2009).
  59. C. R. Galley and M. Tiglio, Radiation reaction and gravitational waves in the effective field theory approach, Phys. Rev. D 79, 124027 (2009).
  60. J. S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. (N.Y.) 2, 407 (1961).
  61. L. V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)].
  62. B. R. Iyer and C. M. Will, Post-Newtonian Gravitational Radiation Reaction for Two-Body Systems, Phys. Rev. Lett. 70, 113 (1993).
  63. B. R. Iyer and C. M. Will, Post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies, Phys. Rev. D 52, 6882 (1995).
  64. C. R. Galley and A. K. Leibovich, Radiation reaction at 3.5 post-Newtonian order in effective field theory, Phys. Rev. D 86, 044029 (2012).
  65. C. R. Galley, Classical Mechanics of Nonconservative Systems, Phys. Rev. Lett. 110, 174301 (2013).
  66. C. R. Galley, D. Tsang, and L. C. Stein, The principle of stationary nonconservative action for classical mechanics and field theories, arXiv:1412.3082.
  67. L. Blanchet and T. Damour, Tail transported temporal correlations in the dynamics of a gravitating system, Phys. Rev. D 37, 1410 (1988).
  68. L. Blanchet and G. Schaefer, Gravitational wave tails and binary star systems, Classical Quantum Gravity 10, 2699 (1993).
  69. L. Blanchet and T. Damour, Hereditary effects in gravitational radiation, Phys. Rev. D 46, 4304 (1992).
  70. L. Blanchet, G. Faye, B. R. Iyer, and S. Sinha, The Third post-Newtonian gravitational wave polarisations and associated spherical harmonic modes for inspiralling compact binaries in quasicircular orbits, Classical Quantum Gravity 25, 165003 (2008); 29, 239501(E) (2012).
  71. L. Blanchet, A. Buonanno, and G. Faye, Tail-induced spin-orbit effect in the gravitational radiation of compact binaries, Phys. Rev. D 84, 064041 (2011).
  72. S. Foffa and R. Sturani, Tail terms in gravitational radiation reaction via effective field theory, Phys. Rev. D 87, 044056 (2013).
  73. K. S. Thorne, Nonradial pulsation of general-relativistic stellar models. IV. The weakfield limit, Astrophys. J. 158, 997 (1969).
  74. W. L. Burke, Gravitational radiation damping of slowly moving systems calculated using matched asymptotic expansions, J. Math. Phys. (N.Y.) 12, 401 (1971).
  75. V. C. de Andrade, L. Blanchet, and G. Faye, Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic coordinate and ADM Hamiltonian formalisms, Classical Quantum Gravity 18, 753 (2001).
  76. D. Bini and T. Damour, Analytical determination of the two-body gravitational interaction potential at the fourth post-Newtonian approximation, Phys. Rev. D 87, 121501 (2013).
  77. C. Galley, A. Leibovich, R. A. Porto, I. Rothstein, and R. Sturani (to be published).
  78. T. Appelquist, M. Dine, and I. J. Muzinich, The static potential in quantum chromodynamics, Phys. Lett. B 69, 231 (1977).
  79. N. Brambilla, A. Pineda, J. Soto, and A. Vairo, The infrared behavior of the static potential in perturbative QCD, Phys. Rev. D 60, 091502 (1999).
  80. N. Brambilla, A. Pineda, J. Soto, and A. Vairo, Potential NRQCD: An Effective theory for heavy quarkonium, Nucl. Phys. B566, 275 (2000).
  81. A. H. Hoang, A. V. Manohar, and I. W. Stewart, The running Coulomb potential and Lamb shift in QCD, Phys. Rev. D 64, 014033 (2001).
  82. A. V. Manohar and I. W. Stewart, The zero-bin and mode factorization in quantum field theory, Phys. Rev. D 76, 074002 (2007).

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Phys. Rev. D 93, 124010– Published 6 June, 2016
  • Received 21 January 2016
Article part of CHORUS

© 2016 American Physical Society

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