- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Tidal effects and renormalization at fourth post-Minkowskian order

Gustav Uhre Jakobsen1,2, Gustav Mogull1,2, Jan Plefka1, and Benjamin Sauer1

  • 1Institut für Physik und IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen Windkanal 2, 12489 Berlin, Germany
  • 2Max Planck Institut für Gravitationsphysik (Albert Einstein Institut), Am Mühlenberg 1, 14476 Potsdam, Germany

PDF

Phys. Rev. D 109, L041504 – Published 20 February, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L041504

Abstract

We determine the adiabatic tidal contributions to the radiation reacted momentum impulse Δpiμ and scattering angle θ between two scattered massive bodies (neutron stars) at next-to-next-to-leading post-Minkowskian order. The state-of-the-art three-loop (fourth post-Mikowskian order) worldline quantum field theory toolkit using dimensional regularization is employed to establish the classical observables. We encounter divergent terms in the gravitoelectric and gravitomagnetic quadrupolar sectors necessitating the addition of postadiabatic counterterms in this classical theory. This leads us to include also the leading postadiabatic tidal contributions to the observables. The resulting renormalization group flow of the associated postadiabatic Love numbers is established and shown to agree with a recent gravitoelectric third post-Newtonian analysis in the nonrelativistic limit.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (125)

  1. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102 (2016).
  2. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), GW170817: Observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119, 161101 (2017).
  3. R. Abbott et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-3: Compact binary coalescences observed by LIGO and Virgo during the second part of the third observing run, Phys. Rev. X 13, 041039 (2023).
  4. P. Amaro-Seoane et al. (LISA Collaboration), Laser interferometer space antenna, arXiv:1702.00786.
  5. M. Punturo et al., The Einstein Telescope: A third-generation gravitational wave observatory, Classical Quantum Gravity 27, 194002 (2010).
  6. S. W. Ballmer et al., Snowmass2021 Cosmic Frontier White Paper: Future gravitational-wave detector facilities, in Snowmass 2021 (2022), 3, arXiv:2203.08228.
  7. L. Blanchet, Gravitational radiation from post-Newtonian sources and inspiralling compact binaries, Living Rev. Relativity 17, 2 (2014).
  8. R. A. Porto, The effective field theorist’s approach to gravitational dynamics, Phys. Rep. 633, 1 (2016).
  9. M. Levi, Effective field theories of post-Newtonian gravity: A comprehensive review, Rep. Prog. Phys. 83, 075901 (2020).
  10. D. A. Kosower, R. Monteiro, and D. O’Connell, The SAGEX review on scattering amplitudes Chapter 14: Classical gravity from scattering amplitudes, J. Phys. A 55, 443015 (2022).
  11. N. E. J. Bjerrum-Bohr, P. H. Damgaard, L. Plante, and P. Vanhove, The SAGEX review on scattering amplitudes Chapter 13: Post-Minkowskian expansion from scattering amplitudes, J. Phys. A 55, 443014 (2022).
  12. A. Buonanno, M. Khalil, D. O’Connell, R. Roiban, M. P. Solon, and M. Zeng, Snowmass White Paper: Gravitational waves and scattering amplitudes, in Snowmass 2021 (2022), 4, arXiv:2204.05194.
  13. P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, The gravitational eikonal: From particle, string and brane collisions to black-hole encounters, arXiv:2306.16488.
  14. G. U. Jakobsen, Gravitational scattering of compact bodies from worldline quantum field theory, other thesis, 8, 2023.
  15. Y. Mino, M. Sasaki, and T. Tanaka, Gravitational radiation reaction to a particle motion, Phys. Rev. D 55, 3457 (1997).
  16. E. Poisson, A. Pound, and I. Vega, The motion of point particles in curved spacetime, Living Rev. Relativity 14, 7 (2011).
  17. L. Barack and A. Pound, Self-force and radiation reaction in general relativity, Rep. Prog. Phys. 82, 016904 (2019).
  18. S. E. Gralla and K. Lobo, Self-force effects in post-Minkowskian scattering, Classical Quantum Gravity 39, 095001 (2022).
  19. A. Buonanno and T. Damour, Effective one-body approach to general relativistic two-body dynamics, Phys. Rev. D 59, 084006 (1999).
  20. A. Buonanno and T. Damour, Transition from inspiral to plunge in binary black hole coalescences, Phys. Rev. D 62, 064015 (2000).
  21. F. Pretorius, Evolution of binary black hole spacetimes, Phys. Rev. Lett. 95, 121101 (2005).
  22. M. Boyle et al., The SXS Collaboration catalog of binary black hole simulations, Classical Quantum Gravity 36, 195006 (2019).
  23. T. Damour, F. Guercilena, I. Hinder, S. Hopper, A. Nagar, and L. Rezzolla, Strong-field scattering of two black holes: Numerics versus analytics, Phys. Rev. D 89, 081503 (2014).
  24. S. J. Kovacs and K. S. Thorne, The generation of gravitational waves. 4. Bremsstrahlung, Astrophys. J. 224, 62 (1978).
  25. K. Westpfahl and M. Goller, Gravitational scattering of two relativistic particles in postlinear approximation, Lett. Nuovo Cimento 26, 573 (1979).
  26. L. Bel, T. Damour, N. Deruelle, J. Ibanez, and J. Martin, Poincaré-invariant gravitational field and equations of motion of two pointlike objects: The postlinear approximation of general relativity, Gen. Relativ. Gravit. 13, 963 (1981).
  27. T. Damour, High-energy gravitational scattering and the general relativistic two-body problem, Phys. Rev. D 97, 044038 (2018).
  28. S. Hopper, A. Nagar, and P. Rettegno, Strong-field scattering of two spinning black holes: Numerics versus analytics, Phys. Rev. D 107, 124034 (2023).
  29. C. Cheung, I. Z. Rothstein, and M. P. Solon, From scattering amplitudes to classical potentials in the post-Minkowskian expansion, Phys. Rev. Lett. 121, 251101 (2018).
  30. G. Kälin and R. A. Porto, From boundary data to bound states, J. High Energy Phys. 01 (2020) 072.
  31. G. Kälin and R. A. Porto, From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist), J. High Energy Phys. 02 (2020) 120.
  32. M. V. S. Saketh, J. Vines, J. Steinhoff, and A. Buonanno, Conservative and radiative dynamics in classical relativistic scattering and bound systems, Phys. Rev. Res. 4, 013127 (2022).
  33. R. Gonzo and C. Shi, Boundary to bound dictionary for generic Kerr orbits, Phys. Rev. D 108, 084065 (2023).
  34. G. Cho, G. Kälin, and R. A. Porto, From boundary data to bound states. Part III. Radiative effects, J. High Energy Phys. 04 (2022) 154.
  35. W. D. Goldberger and I. Z. Rothstein, An effective field theory of gravity for extended objects, Phys. Rev. D 73, 104029 (2006).
  36. G. Kälin and R. A. Porto, Post-Minkowskian effective field theory for conservative binary dynamics, J. High Energy Phys. 11 (2020) 106.
  37. G. Kälin, Z. Liu, and R. A. Porto, Conservative dynamics of binary systems to third post-Minkowskian order from the effective field theory approach, Phys. Rev. Lett. 125, 261103 (2020).
  38. G. Kälin, Z. Liu, and R. A. Porto, Conservative tidal effects in compact binary systems to next-to-leading post-Minkowskian order, Phys. Rev. D 102, 124025 (2020).
  39. C. Dlapa, G. Kälin, Z. Liu, and R. A. Porto, Dynamics of binary systems to fourth Post-Minkowskian order from the effective field theory approach, Phys. Lett. B 831, 137203 (2022).
  40. C. Dlapa, G. Kälin, Z. Liu, and R. A. Porto, Conservative dynamics of binary systems at fourth post-Minkowskian order in the large-eccentricity expansion, Phys. Rev. Lett. 128, 161104 (2022).
  41. Z. Liu, R. A. Porto, and Z. Yang, Spin effects in the effective field theory approach to post-Minkowskian conservative dynamics, J. High Energy Phys. 06 (2021) 012.
  42. S. Mougiakakos, M. M. Riva, and F. Vernizzi, Gravitational Bremsstrahlung in the post-Minkowskian effective field theory, Phys. Rev. D 104, 024041 (2021).
  43. M. M. Riva and F. Vernizzi, Radiated momentum in the post-Minkowskian worldline approach via reverse unitarity, J. High Energy Phys. 11 (2021) 228.
  44. S. Mougiakakos, M. M. Riva, and F. Vernizzi, Gravitational bremsstrahlung with tidal effects in the post-Minkowskian expansion, Phys. Rev. Lett. 129, 121101 (2022).
  45. M. M. Riva, F. Vernizzi, and L. K. Wong, Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion, Phys. Rev. D 106, 044013 (2022).
  46. G. Mogull, J. Plefka, and J. Steinhoff, Classical black hole scattering from a worldline quantum field theory, J. High Energy Phys. 02 (2021) 048.
  47. G. U. Jakobsen, G. Mogull, J. Plefka, and J. Steinhoff, Classical gravitational bremsstrahlung from a worldline quantum field theory, Phys. Rev. Lett. 126, 201103 (2021).
  48. G. U. Jakobsen, G. Mogull, J. Plefka, and J. Steinhoff, Gravitational bremsstrahlung and hidden supersymmetry of spinning bodies, Phys. Rev. Lett. 128, 011101 (2022).
  49. G. U. Jakobsen, G. Mogull, J. Plefka, and J. Steinhoff, SUSY in the sky with gravitons, J. High Energy Phys. 01 (2022) 027.
  50. G. U. Jakobsen and G. Mogull, Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory, Phys. Rev. Lett. 128, 141102 (2022).
  51. G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, All things retarded: Radiation-reaction in worldline quantum field theory, J. High Energy Phys. 10 (2022) 128.
  52. C. Shi and J. Plefka, Classical double copy of worldline quantum field theory, Phys. Rev. D 105, 026007 (2022).
  53. F. Bastianelli, F. Comberiati, and L. de la Cruz, Light bending from eikonal in worldline quantum field theory, J. High Energy Phys. 02 (2022) 209.
  54. F. Comberiati and C. Shi, Classical double copy of spinning worldline quantum field theory, J. High Energy Phys. 04 (2023) 008.
  55. T. Wang, Binary dynamics from worldline QFT for scalar QED, Phys. Rev. D 107, 085011 (2023).
  56. D. Neill and I. Z. Rothstein, Classical space-times from the S matrix, Nucl. Phys. B877, 177 (2013).
  57. A. Luna, I. Nicholson, D. O’Connell, and C. D. White, Inelastic black hole scattering from charged scalar amplitudes, J. High Energy Phys. 03 (2018) 044.
  58. D. A. Kosower, B. Maybee, and D. O’Connell, Amplitudes, observables, and classical scattering, J. High Energy Phys. 02 (2019) 137.
  59. A. Cristofoli, R. Gonzo, D. A. Kosower, and D. O’Connell, Waveforms from amplitudes, Phys. Rev. D 106, 056007 (2022).
  60. N. E. J. Bjerrum-Bohr, J. F. Donoghue, and P. Vanhove, On-shell techniques and universal results in quantum gravity, J. High Energy Phys. 02 (2014) 111.
  61. N. E. J. Bjerrum-Bohr, P. H. Damgaard, G. Festuccia, L. Planté, and P. Vanhove, General relativity from scattering amplitudes, Phys. Rev. Lett. 121, 171601 (2018).
  62. Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, Scattering amplitudes and the conservative Hamiltonian for binary systems at third post-Minkowskian order, Phys. Rev. Lett. 122, 201603 (2019).
  63. Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, Black hole binary dynamics from the double copy and effective theory, J. High Energy Phys. 10 (2019) 206.
  64. N. E. J. Bjerrum-Bohr, L. Planté, and P. Vanhove, Post-Minkowskian radial action from soft limits and velocity cuts, J. High Energy Phys. 03 (2022) 071.
  65. C. Cheung and M. P. Solon, Classical gravitational scattering at O(G3) from Feynman diagrams, J. High Energy Phys. 06 (2020) 144.
  66. N. E. J. Bjerrum-Bohr, P. H. Damgaard, L. Planté, and P. Vanhove, The amplitude for classical gravitational scattering at third Post-Minkowskian order, J. High Energy Phys. 08 (2021) 172.
  67. P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, Universality of ultra-relativistic gravitational scattering, Phys. Lett. B 811, 135924 (2020).
  68. P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, The eikonal approach to gravitational scattering and radiation at O(G3), J. High Energy Phys. 07 (2021) 169.
  69. P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, Radiation reaction from soft theorems, Phys. Lett. B 818, 136379 (2021).
  70. P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, Classical gravitational observables from the Eikonal operator, Phys. Lett. B 843, 138049 (2023).
  71. C. Heissenberg, Angular momentum loss due to tidal effects in the post-Minkowskian expansion, Phys. Rev. Lett. 131, 011603 (2023).
  72. T. Damour, Radiative contribution to classical gravitational scattering at the third order in G, Phys. Rev. D 102, 124008 (2020).
  73. E. Herrmann, J. Parra-Martinez, M. S. Ruf, and M. Zeng, Radiative classical gravitational observables at O(G3) from scattering amplitudes, J. High Energy Phys. 10 (2021) 148.
  74. P. H. Damgaard, K. Haddad, and A. Helset, Heavy black hole effective theory, J. High Energy Phys. 11 (2019) 070.
  75. P. H. Damgaard, L. Plante, and P. Vanhove, On an exponential representation of the gravitational S-matrix, J. High Energy Phys. 11 (2021) 213.
  76. P. H. Damgaard, E. R. Hansen, L. Planté, and P. Vanhove, The relation between KMOC and worldline formalisms for classical gravity, J. High Energy Phys. 09 (2023) 059.
  77. R. Aoude, K. Haddad, and A. Helset, On-shell heavy particle effective theories, J. High Energy Phys. 05 (2020) 051.
  78. M. Accettulli Huber, A. Brandhuber, S. De Angelis, and G. Travaglini, From amplitudes to gravitational radiation with cubic interactions and tidal effects, Phys. Rev. D 103, 045015 (2021).
  79. A. Brandhuber, G. Chen, G. Travaglini, and C. Wen, Classical gravitational scattering from a gauge-invariant double copy, J. High Energy Phys. 10 (2021) 118.
  80. Z. Bern, D. Kosmopoulos, A. Luna, R. Roiban, and F. Teng, Binary dynamics through the fifth power of spin at O(G2), Phys. Rev. Lett. 130, 201402 (2023).
  81. R. Aoude, K. Haddad, and A. Helset, Classical gravitational spinning-spinless scattering at O(G2S∞), Phys. Rev. Lett. 129, 141102 (2022).
  82. R. Aoude, K. Haddad, and A. Helset, Classical gravitational scattering amplitude at O(G2S1∞S2∞), Phys. Rev. D 108, 024050 (2023).
  83. Y. F. Bautista, Dynamics for super-extremal Kerr binary systems at O(G2), Phys. Rev. D 108, 084036 (2023).
  84. P. H. Damgaard, E. R. Hansen, L. Planté, and P. Vanhove, Classical observables from the exponential representation of the gravitational S-matrix, J. High Energy Phys. 09 (2023) 183.
  85. A. Brandhuber, G. R. Brown, G. Chen, S. De Angelis, J. Gowdy, and G. Travaglini, One-loop gravitational bremsstrahlung and waveforms from a heavy-mass effective field theory, J. High Energy Phys. 06 (2023) 048.
  86. A. Herderschee, R. Roiban, and F. Teng, The sub-leading scattering waveform from amplitudes, J. High Energy Phys. 06 (2023) 004.
  87. A. Georgoudis, C. Heissenberg, and I. Vazquez-Holm, Inelastic exponentiation and classical gravitational scattering at one loop, J. High Energy Phys. 06 (2023) 126.
  88. A. Elkhidir, D. O’Connell, M. Sergola, and I. A. Vazquez-Holm, Radiation and reaction at one loop, arXiv:2303.06211.
  89. S. Caron-Huot, M. Giroux, H. S. Hannesdottir, and S. Mizera, What can be measured asymptotically?, arXiv:2308.02125.
  90. E. E. Flanagan and T. Hinderer, Constraining neutron star tidal Love numbers with gravitational wave detectors, Phys. Rev. D 77, 021502 (2008).
  91. T. Hinderer, Tidal Love numbers of neutron stars, Astrophys. J. 677, 1216 (2008).
  92. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Properties of the binary neutron star merger GW170817, Phys. Rev. X 9, 011001 (2019).
  93. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), GW170817: Measurements of neutron star radii and equation of state, Phys. Rev. Lett. 121, 161101 (2018).
  94. K. Chatziioannou, Neutron star tidal deformability and equation of state constraints, Gen. Relativ. Gravit. 52, 109 (2020).
  95. B. K. Pradhan, A. Vijaykumar, and D. Chatterjee, Impact of updated multipole Love numbers and f-Love universal relations in the context of binary neutron stars, Phys. Rev. D 107, 023010 (2023).
  96. C. M. Will, Tidal gravitational radiation from homogeneous stars, Astrophys. J. 274, 858 (1983).
  97. J. Steinhoff, T. Hinderer, A. Buonanno, and A. Taracchini, Dynamical tides in general relativity: Effective action and effective-one-body Hamiltonian, Phys. Rev. D 94, 104028 (2016).
  98. G. Pratten, P. Schmidt, and N. Williams, Impact of dynamical tides on the reconstruction of the neutron star equation of state, Phys. Rev. Lett. 129, 081102 (2022).
  99. D. Bini, T. Damour, and G. Faye, Effective action approach to higher-order relativistic tidal interactions in binary systems and their effective one body description, Phys. Rev. D 85, 124034 (2012).
  100. Q. Henry, G. Faye, and L. Blanchet, Tidal effects in the equations of motion of compact binary systems to next-to-next-to-leading post-Newtonian order, Phys. Rev. D 101, 064047 (2020).
  101. M. V. S. Saketh, Z. Zhou, and M. M. Ivanov, Dynamical tidal response of Kerr black holes from scattering amplitudes, arXiv:2307.10391.
  102. M. K. Mandal, P. Mastrolia, H. O. Silva, R. Patil, and J. Steinhoff, Renormalizing Love: Tidal effects at the third post-Newtonian order, arXiv:2308.01865.
  103. D. Bini, T. Damour, and A. Geralico, Scattering of tidally interacting bodies in post-Minkowskian gravity, Phys. Rev. D 101, 044039 (2020).
  104. C. Cheung and M. P. Solon, Tidal effects in the post-Minkowskian expansion, Phys. Rev. Lett. 125, 191601 (2020).
  105. K. Haddad and A. Helset, Tidal effects in quantum field theory, J. High Energy Phys. 12 (2020) 024.
  106. Z. Bern, J. Parra-Martinez, R. Roiban, E. Sawyer, and C.-H. Shen, Leading nonlinear tidal effects and scattering amplitudes, J. High Energy Phys. 05 (2021) 188.
  107. L. Blanchet, Gravitational wave tails of tails, Classical Quantum Gravity 15, 113 (1998).
  108. W. D. Goldberger and A. Ross, Gravitational radiative corrections from effective field theory, Phys. Rev. D 81, 124015 (2010).
  109. H. Fang and G. Lovelace, Tidal coupling of a Schwarzschild black hole and circularly orbiting moon, Phys. Rev. D 72, 124016 (2005).
  110. T. Damour and A. Nagar, Relativistic tidal properties of neutron stars, Phys. Rev. D 80, 084035 (2009).
  111. T. Binnington and E. Poisson, Relativistic theory of tidal Love numbers, Phys. Rev. D 80, 084018 (2009).
  112. P. Rettegno, G. Pratten, L. Thomas, P. Schmidt, and T. Damour, Strong-field scattering of two spinning black holes: Numerical Relativity versus post-Minkowskian gravity, Phys. Rev. D 108, 124016 (2023).
  113. G. U. Jakobsen, G. Mogull, J. Plefka, B. Sauer, and Y. Xu, Conservative scattering of spinning black holes at fourth post-Minkowskian order, Phys. Rev. Lett. 131, 151401 (2023).
  114. G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, Dissipative scattering of spinning black holes at fourth post-Minkowskian order, Phys. Rev. Lett. 131, 241402 (2023).
  115. G. Kälin, J. Neef, and R. A. Porto, Radiation-reaction in the effective field theory approach to post-Minkowskian dynamics, J. High Energy Phys. 01 (2023) 140.
  116. D. G. Boulware and L. S. Brown, Tree graphs and classical fields, Phys. Rev. 172, 1628 (1968).
  117. B. Ruijl, T. Ueda, and J. Vermaseren, FORM version 4.2, arXiv:1707.06453.
  118. T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B580, 485 (2000).
  119. J. M. Henn, Multiloop integrals in dimensional regularization made simple, Phys. Rev. Lett. 110, 251601 (2013).
  120. M. Beneke and V. A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B522, 321 (1998).
  121. Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.-H. Shen, M. P. Solon, and M. Zeng, Scattering amplitudes, the tail effect, and conservative binary dynamics at O(G4), Phys. Rev. Lett. 128, 161103 (2022).
  122. C. Dlapa, G. Kälin, Z. Liu, J. Neef, and R. A. Porto, Radiation reaction and gravitational waves at fourth post-Minkowskian order, Phys. Rev. Lett. 130, 101401 (2023).
  123. C. Dlapa, G. Kälin, Z. Liu, and R. A. Porto, Bootstrapping the relativistic two-body problem, J. High Energy Phys. 08 (2023) 109.
  124. M. K. Mandal, P. Mastrolia, H. O. Silva, R. Patil, and J. Steinhoff, Gravitoelectric dynamical tides at second post-Newtonian order, J. High Energy Phys. 11 (2023) 067.
  125. T. Hinderer et al., Effects of neutron-star dynamic tides on gravitational waveforms within the effective-one-body approach, Phys. Rev. Lett. 116, 181101 (2016).

Outline

Information

Phys. Rev. D 109, L041504– Published 20 February, 2024
  • Received 4 January 2024
  • Accepted 19 January 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation