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  • Letter
  • Open Access

Superrotations at spacelike infinity

Adrien Fiorucci1,*, Javier Matulich2,†, and Romain Ruzziconi3,‡

  • *Contact author: adrien.fiorucci@tuwien.ac.at
  • †Contact author: javier.matulich@csic.es
  • ‡Contact author: romain.ruzziconi@maths.ox.ac.uk
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Phys. Rev. D 110, L061502 – Published 13 September, 2024

DOI: https://doi.org/10.1103/PhysRevD.110.L061502

Abstract

We propose a consistent set of boundary conditions for gravity in asymptotically flat spacetime at spacelike infinity, which yields an enhancement of the Bondi-Metzner-Sachs group with smooth superrotations and new subleading symmetries. These boundary conditions are obtained by allowing fluctuations of the boundary structure which are responsible for divergences in the symplectic form, and a renormalization procedure is required to obtain finite canonical generators. The latter are then made integrable by incorporating boundary terms into the symplectic structure, which naturally derive from a linearized spin-two boundary field on a curved background with positive cosmological constant. Finally, we show that the canonical generators form a nonlinear algebra under the Poisson bracket and verify the consistency of this structure with the Jacobi identity.

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References (105)

  1. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. R. Soc. A 269, 21 (1962).
  2. R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128, 2851 (1962).
  3. G. Barnich and C. Troessaert, Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited, Phys. Rev. Lett. 105, 111103 (2010).
  4. G. Barnich and C. Troessaert, Supertranslations call for superrotations, Proc. Sci. CNCFG2010 (2010) 010 [arXiv:1102.4632].
  5. G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, J. High Energy Phys. 05 (2010) 062.
  6. G. Barnich and C. Troessaert, BMS charge algebra, J. High Energy Phys. 12 (2011) 105.
  7. G. Barnich and C. Troessaert, Comments on holographic current algebras and asymptotically flat four dimensional spacetimes at null infinity, J. High Energy Phys. 11 (2013) 003.
  8. E. E. Flanagan and D. A. Nichols, Conserved charges of the extended Bondi-Metzner-Sachs algebra, Phys. Rev. D 95, 044002 (2017).
  9. G. Barnich, P. Mao, and R. Ruzziconi, BMS current algebra in the context of the Newman–Penrose formalism, Classical Quantum Gravity 37, 095010 (2020).
  10. G. Barnich and R. Ruzziconi, Coadjoint representation of the BMS group on celestial Riemann surfaces, J. High Energy Phys. 06 (2021) 079.
  11. M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90, 124028 (2014).
  12. M. Campiglia and A. Laddha, New symmetries for the gravitational S-matrix, J. High Energy Phys. 04 (2015) 076.
  13. G. Compère, A. Fiorucci, and R. Ruzziconi, Superboost transitions, refraction memory and super-Lorentz charge algebra, J. High Energy Phys. 11 (2018) 200.
  14. E. E. Flanagan, K. Prabhu, and I. Shehzad, Extensions of the asymptotic symmetry algebra of general relativity, J. High Energy Phys. 01 (2020) 002.
  15. M. Campiglia and J. Peraza, Generalized BMS charge algebra, Phys. Rev. D 101, 104039 (2020).
  16. L. Freidel, R. Oliveri, D. Pranzetti, and S. Speziale, The Weyl BMS group and Einstein’s equations, J. High Energy Phys. 07 (2021) 170.
  17. L. Freidel, R. Oliveri, D. Pranzetti, and S. Speziale, Extended corner symmetry, charge bracket and Einstein’s equations, J. High Energy Phys. 09 (2021) 083.
  18. R. Ruzziconi, On the various extensions of the BMS group, Ph.D. thesis, University of Brussels, 2020.
  19. A. Fiorucci, Leaky covariant phase spaces: Theory and application to Λ-BMS symmetry, Ph.D. thesis, Brussels University, International Solvay Institutes, Brussels, 2021.
  20. A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory (Princeton University Press, Princeton, NJ, 2018).
  21. A. Strominger, On BMS invariance of gravitational scattering, J. High Energy Phys. 07 (2014) 152.
  22. T. He, V. Lysov, P. Mitra, and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, J. High Energy Phys. 05 (2015) 151.
  23. F. Cachazo and A. Strominger, Evidence for a new soft graviton theorem, arXiv:1404.4091.
  24. D. Kapec, V. Lysov, S. Pasterski, and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity S-matrix, J. High Energy Phys. 08 (2014) 058.
  25. T. Adamo, E. Casali, and D. Skinner, Perturbative gravity at null infinity, Classical Quantum Gravity 31, 225008 (2014).
  26. Z. Bern, S. Davies, and J. Nohle, On loop corrections to subleading soft behavior of gluons and gravitons, Phys. Rev. D 90, 085015 (2014).
  27. T. He, D. Kapec, A.-M. Raclariu, and A. Strominger, Loop-corrected virasoro symmetry of 4D quantum gravity, J. High Energy Phys. 08 (2017) 050.
  28. A. Laddha and A. Sen, Logarithmic terms in the soft expansion in four dimensions, J. High Energy Phys. 10 (2018) 056.
  29. B. Sahoo and A. Sen, Classical and quantum results on logarithmic terms in the soft theorem in four dimensions, J. High Energy Phys. 02 (2019) 086.
  30. L. Donnay and R. Ruzziconi, BMS flux algebra in celestial holography, J. High Energy Phys. 11 (2021) 040.
  31. L. Donnay, K. Nguyen, and R. Ruzziconi, Loop-corrected subleading soft theorem and the celestial stress tensor, J. High Energy Phys. 09 (2022) 063.
  32. S. Pasterski, A comment on loop corrections to the celestial stress tensor, J. High Energy Phys. 01 (2023) 025.
  33. S. Agrawal, L. Donnay, K. Nguyen, and R. Ruzziconi, Logarithmic soft graviton theorems from superrotation Ward identities, J. High Energy Phys. 02 (2024) 120.
  34. S. Choi, A. Laddha, and A. Puhm, Asymptotic symmetries for logarithmic soft theorems in gauge theory and gravity, arXiv:2403.13053.
  35. A. M. Grant and D. A. Nichols, Outlook for detecting the gravitational-wave displacement and spin memory effects with current and future gravitational-wave detectors, Phys. Rev. D 107, 064056 (2023).
  36. A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, J. High Energy Phys. 01 (2016) 086.
  37. S. Pasterski, A. Strominger, and A. Zhiboedov, New gravitational memories, J. High Energy Phys. 12 (2016) 053.
  38. D. A. Nichols, Center-of-mass angular momentum and memory effect in asymptotically flat spacetimes, Phys. Rev. D 98, 064032 (2018).
  39. T. Regge and C. Teitelboim, Role of surface integrals in the Hamiltonian formulation of general relativity, Ann. Phys. (N.Y.) 88, 286 (1974).
  40. C. Troessaert, The BMS4 algebra at spatial infinity, Classical Quantum Gravity 35, 074003 (2018).
  41. M. Henneaux and C. Troessaert, BMS group at spatial infinity: The Hamiltonian (ADM) approach, J. High Energy Phys. 03 (2018) 147.
  42. M. Henneaux and C. Troessaert, Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity, J. High Energy Phys. 07 (2018) 171.
  43. M. Henneaux and C. Troessaert, The asymptotic structure of gravity at spatial infinity in four spacetime dimensions, Proc. Steklov Inst. Math. 309, 127 (2020).
  44. H. Friedrich, Peeling or not peeling—Is that the question?, Classical Quantum Gravity 35, 083001 (2018).
  45. L. M. A. Kehrberger, The case against smooth null infinity I: Heuristics and counter-examples, Ann. Henri Poincare 23, 829 (2022).
  46. L. M. A. Kehrberger, The case against smooth null infinity II: A logarithmically modified Price’s law, arXiv:2105.08084.
  47. J. A. Valiente-Kroon, A new class of obstructions to the smoothness of null infinity, Commun. Math. Phys. 244, 133 (2004).
  48. P. T. Chrusciel, M. A. H. MacCallum, and D. B. Singleton, Gravitational waves in general relativity: 14. Bondi expansions and the polyhomogeneity of Scri, Proc. R. Soc. A 436, 299 (1992).
  49. P. T. Chrusciel and E. Delay, Existence of nontrivial, vacuum, asymptotically simple space-times, Classical Quantum Gravity 19, L71 (2002).
  50. G. Compère and A. Fiorucci, Asymptotically flat spacetimes with BMS3 symmetry, Classical Quantum Gravity 34, 204002 (2017).
  51. F. Capone, K. Nguyen, and E. Parisini, Charge and antipodal matching across spatial infinity, SciPost Phys. 14, 014 (2023).
  52. G. Compère, S. E. Gralla, and H. Wei, An asymptotic framework for gravitational scattering, Classical Quantum Gravity 40, 205018 (2023).
  53. K. Prabhu, Conservation of asymptotic charges from past to future null infinity: Supermomentum in general relativity, J. High Energy Phys. 03 (2019) 148.
  54. K. Prabhu and I. Shehzad, Conservation of asymptotic charges from past to future null infinity: Lorentz charges in general relativity, J. High Energy Phys. 08 (2022) 029.
  55. M. M. A. Mohamed, K. Prabhu, and J. A. V. Kroon, BMS-supertranslation charges at the critical sets of null infinity, J. Math. Phys. (N.Y.) 65, 032501 (2024).
  56. R. Beig, Integration of Einstein’s equations near spatial infinity, Proc. R. Soc. A 391, 295 (1984).
  57. R. Beig and B. Schmidt, Einstein’s equations near spatial infinity, Commun. Math. Phys. 87, 65 (1982).
  58. A. Ashtekar and J. D. Romano, Spatial infinity as a boundary of space-time, Classical Quantum Gravity 9, 1069 (1992).
  59. S. de Haro, S. N. Solodukhin, and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217, 595 (2001).
  60. I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes, J. High Energy Phys. 08 (2005) 004.
  61. R. B. Mann and D. Marolf, Holographic renormalization of asymptotically flat spacetimes, Classical Quantum Gravity 23, 2927 (2006).
  62. G. Compere and D. Marolf, Setting the boundary free in AdS/CFT, Classical Quantum Gravity 25, 195014 (2008).
  63. A. Fiorucci and R. Ruzziconi, Charge algebra in Al(A)dSn spacetimes, J. High Energy Phys. 05 (2021) 210.
  64. G. Compère, A. Fiorucci, and R. Ruzziconi, The Λ−BMS4 charge algebra, J. High Energy Phys. 10 (2020) 205.
  65. R. Ruzziconi and C. Zwikel, Conservation and integrability in lower-dimensional gravity, J. High Energy Phys. 04 (2021) 034.
  66. V. Chandrasekaran, E. E. Flanagan, I. Shehzad, and A. J. Speranza, A general framework for gravitational charges and holographic renormalization, Int. J. Mod. Phys. A 37, 2250105 (2022).
  67. D. Grumiller, R. Ruzziconi, and C. Zwikel, Generalized dilaton gravity in 2d, SciPost Phys. 12, 032 (2022).
  68. M. Geiller, C. Goeller, and C. Zwikel, 3d gravity in Bondi-Weyl gauge: Charges, corners, and integrability, J. High Energy Phys. 09 (2021) 029.
  69. M. Geiller and C. Zwikel, The partial Bondi gauge: Further enlarging the asymptotic structure of gravity, SciPost Phys. 13, 108 (2022).
  70. A. Campoleoni, L. Ciambelli, A. Delfante, C. Marteau, P. M. Petropoulos, and R. Ruzziconi, Holographic Lorentz and Carroll frames, J. High Energy Phys. 12 (2022) 007.
  71. R. McNees and C. Zwikel, Finite charges from the bulk action, J. High Energy Phys. 08 (2023) 154.
  72. F. Capone, P. Mitra, A. Poole, and B. Tomova, Phase space renormalization and finite BMS charges in six dimensions, J. High Energy Phys. 11 (2023) 034.
  73. L. Freidel and A. Riello, Renormalization of conformal infinity as a stretched horizon, arXiv:2402.03097.
  74. G. Barnich and G. Compère, Surface charge algebra in gauge theories and thermodynamic integrability, J. Math. Phys. (N.Y.) 49, 042901 (2008).
  75. D. Grumiller, A. Pérez, M. Sheikh-Jabbari, R. Troncoso, and C. Zwikel, Spacetime structure near generic horizons and soft hair, Phys. Rev. Lett. 124, 041601 (2020).
  76. H. Adami, M. M. Sheikh-Jabbari, V. Taghiloo, H. Yavartanoo, and C. Zwikel, Symmetries at null boundaries: Two and three dimensional gravity cases, J. High Energy Phys. 10 (2020) 107.
  77. D. Grumiller, R. Ruzziconi, and C. Zwikel, One-loop partition function of gravity with leaky boundary conditions, J. High Energy Phys. 02 (2024) 080.
  78. F. Alessio, G. Barnich, L. Ciambelli, P. Mao, and R. Ruzziconi, Weyl charges in asymptotically locally AdS3 spacetimes, Phys. Rev. D 103, 046003 (2021).
  79. H. Adami, D. Grumiller, S. Sadeghian, M. M. Sheikh-Jabbari, and C. Zwikel, T-Witts from the horizon, J. High Energy Phys. 04 (2020) 128.
  80. H. Adami, D. Grumiller, M. M. Sheikh-Jabbari, V. Taghiloo, H. Yavartanoo, and C. Zwikel, Null boundary phase space: Slicings, news & memory, J. High Energy Phys. 11 (2021) 155.
  81. M. Henneaux and C. Troessaert, Asymptotic symmetries of electromagnetism at spatial infinity, J. High Energy Phys. 05 (2018) 137.
  82. O. Fuentealba, M. Henneaux, S. Majumdar, J. Matulich, and T. Neogi, Asymptotic structure of the Rarita-Schwinger theory in four spacetime dimensions at spatial infinity, J. High Energy Phys. 02 (2021) 031.
  83. O. Fuentealba, M. Henneaux, S. Majumdar, J. Matulich, and T. Neogi, Local supersymmetry and the square roots of Bondi-Metzner-Sachs supertranslations, Phys. Rev. D 104, L121702 (2021).
  84. O. Fuentealba, M. Henneaux, J. Matulich, and C. Troessaert, Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis, J. High Energy Phys. 07 (2022) 149.
  85. O. Fuentealba, M. Henneaux, J. Matulich, and C. Troessaert, Bondi-Metzner-Sachs group in five spacetime dimensions, Phys. Rev. Lett. 128, 051103 (2022).
  86. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.110.L061502 for technical and intermediate results: (1) the transformation laws of the fields under hypersurface deformations, (2) the computation of the symplectic structure and the Hamiltonian generators, and (3) some elements from the boundary spin-two theory.
  87. P. A. M. Dirac, The theory of gravitation in Hamiltonian form, Proc. R. Soc. A 246, 333 (1958).
  88. R. L. Arnowitt, S. Deser, and C. W. Misner, The dynamics of general relativity, Gen. Relativ. Gravit. 40, 1997 (2008).
  89. A. J. Hanson, T. Regge, and C. Teitelboim, Constrained Hamiltonian Systems (Accademia Nazionale dei Lincei, New York, 1976).
  90. I. Bengtsson, Note on massive spin-2 in curved space, J. Math. Phys. (N.Y.) 36, 5805 (1995).
  91. H. Friedrich, Gravitational fields near space-like and null infinity, J. Geom. Phys. 24, 83 (1998).
  92. M. Crainic and R. L. Fernandes, Integrability of Lie brackets, Ann. Math. 157, 575 (2004).
  93. G. Barnich, Centrally extended BMS4 Lie algebroid, J. High Energy Phys. 06 (2017) 007.
  94. L. Baulieu and T. Wetzstein, BRST BMS4 symmetry and its cocycles from horizontality conditions, J. High Energy Phys. 07 (2023) 130.
  95. G. Compère, A. Fiorucci, and R. Ruzziconi, The Λ−BMS4 group of dS4 and new boundary conditions for AdS4, Classical Quantum Gravity 36, 195017 (2019); 38, 229501(E) (2021).
  96. G. Compere and F. Dehouck, Relaxing the parity conditions of asymptotically flat gravity, Classical Quantum Gravity 28, 245016 (2011); 30, 039501(E) (2013).
  97. L. Ciambelli, C. Marteau, P. M. Petropoulos, and R. Ruzziconi, Fefferman-Graham and Bondi gauges in the fluid/gravity correspondence, Proc. Sci. CORFU2019 (2020) 154 [arXiv:2006.10083].
  98. L. Ciambelli, C. Marteau, P. M. Petropoulos, and R. Ruzziconi, Gauges in three-dimensional gravity and holographic fluids, J. High Energy Phys. 11 (2020) 092.
  99. M. Geiller and C. Zwikel, The partial Bondi gauge: Gauge fixings and asymptotic charges, SciPost Phys. 16, 076 (2024).
  100. P. Mao and W. Zhao, Twisting asymptotic symmetries and algebraically special vacuum solutions, J. High Energy Phys. 03 (2024) 166.
  101. W. Donnelly and L. Freidel, Local subsystems in gauge theory and gravity, J. High Energy Phys. 09 (2016) 102.
  102. L. Freidel, M. Geiller, and D. Pranzetti, Edge modes of gravity. Part I. Corner potentials and charges, J. High Energy Phys. 11 (2020) 026.
  103. W. Donnelly, L. Freidel, S. F. Moosavian, and A. J. Speranza, Gravitational edge modes, coadjoint orbits, and hydrodynamics, J. High Energy Phys. 09 (2021) 008.
  104. L. Ciambelli, R. G. Leigh, and P.-C. Pai, Embeddings and integrable charges for extended corner symmetry, Phys. Rev. Lett. 128, 171302 (2022).
  105. L. Freidel, A canonical bracket for open gravitational system, arXiv:2111.14747.

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Phys. Rev. D 110, L061502– Published 13 September, 2024
  • Received 14 May 2024
  • Accepted 15 August 2024
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