Abstract
We present a new set of asymptotic conditions for gravity at spatial infinity that includes gravitational magnetic-type solutions, allows for a non-trivial Hamiltonian action of the complete BM S4 algebra, and leads to a non-divergent behaviour of the Weyl tensor as one approaches null infinity. We then extend the analysis to the coupled Einstein-Maxwell system and obtain as canonically realized asymptotic symmetry algebra a semi-direct sum of the BM S4 algebra with the angle dependent u(1) transformations. The Hamiltonian charge-generator associated with each asymptotic symmetry element is explicitly written. The connection with matching conditions at null infinity is also discussed.
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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. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
R.K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103 [INSPIRE].
R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) 2851 [INSPIRE].
R. Penrose, Asymptotic properties of fields and space-times, Phys. Rev. Lett. 10 (1963) 66 [INSPIRE].
T. Mädler and J. Winicour, Bondi-Sachs formalism, Scholarpedia 11 (2016) 33528 [arXiv:1609.01731] [INSPIRE].
F. Alessio and G. Esposito, On the structure and applications of the Bondi-Metzner-Sachs group, Int. J. Geom. Meth. Mod. Phys. 15 (2017) 1830002 [arXiv:1709.05134] [INSPIRE].
A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448 [INSPIRE].
T. Dray and M. Streubel, Angular momentum at null infinity, Class. Quant. Grav. 1 (1984) 15.
R.M. Wald and A. Zoupas, A general definition of ‘conserved quantities’ in general relativity and other theories of gravity, Phys. Rev. D 61 (2000) 084027 [gr-qc/9911095] [INSPIRE].
G. Barnich and C. Troessaert, BMS charge algebra, JHEP 12 (2011) 105 [arXiv:1106.0213] [INSPIRE].
C. Bunster, A. Gomberoff and A. Pérez, Regge-Teitelboim analysis of the symmetries of electromagnetic and gravitational fields on asymptotically null spacelike surfaces, arXiv:1805.03728 [INSPIRE].
M. Henneaux and C. Troessaert, BMS group at spatial infinity: the Hamiltonian (ADM) approach, JHEP 03 (2018) 147 [arXiv:1801.03718] [INSPIRE].
C. Troessaert, The BMS 4 algebra at spatial infinity, Class. Quant. Grav. 35 (2018) 074003 [arXiv:1704.06223] [INSPIRE].
M. Henneaux and C. Troessaert, Asymptotic symmetries of electromagnetism at spatial infinity, JHEP 05 (2018) 137 [arXiv:1803.10194] [INSPIRE].
T. Regge and C. Teitelboim, Role of surface integrals in the Hamiltonian formulation of general relativity, Annals Phys. 88 (1974) 286 [INSPIRE].
R. Benguria, P. Cordero and C. Teitelboim, Aspects of the Hamiltonian dynamics of interacting gravitational gauge and Higgs fields with applications to spherical symmetry, Nucl. Phys. B 122 (1977) 61 [INSPIRE].
A. Ashtekar and R.O. Hansen, A unified treatment of null and spatial infinity in general relativity. I — Universal structure, asymptotic symmetries and conserved quantities at spatial infinity, J. Math. Phys. 19 (1978) 1542 [INSPIRE].
R. Beig and B. Schmidt, Einstein’s equations near spatial infinity, Commun. Math. Phys. 87 (1982) 65-
R. Beig, Integration of Einstein’s equations near spatial infinity, Proc. Royal Soc. A 1801 (1984) 295.
A. Ashtekar and J.D. Romano, Spatial infinity as a boundary of space-time, Class. Quant. Grav. 9 (1992) 1069 [INSPIRE].
G. Compere and F. Dehouck, Relaxing the parity conditions of asymptotically flat gravity, Class. Quant. Grav. 28 (2011) 245016 [Erratum ibid. 30 (2013) 039501] [arXiv:1106.4045] [INSPIRE].
H. Friedrich, Gravitational fields near space-like and null infinity, J. Geom. Phys. 24 (1998) 83.
H. Friedrich and J. Kannar, Bondi type systems near space-like infinity and the calculation of the NP constants, J. Math. Phys. 41 (2000) 2195 [gr-qc/9910077] [INSPIRE].
H. Friedrich and J. Kannar, Calculating asymptotic quantities near space-like and null infinity from Cauchy data, Annalen Phys. 9 (2000) 321 [gr-qc/9911103] [INSPIRE].
A. Ashtekar and R. Penrose, Mass positivity from focussing and the structure of spacelike infinity, in Further advances in twistor theory, volume II, L. Mason et al. eds., Longman, London U.K. (1995).
A. Strominger, Asymptotic symmetries of Yang-Mills theory, JHEP 07 (2014) 151 [arXiv:1308.0589] [INSPIRE].
G. Barnich and P.-H. Lambert, Einstein-Yang-Mills theory: asymptotic symmetries, Phys. Rev. D 88 (2013) 103006 [arXiv:1310.2698] [INSPIRE].
A.P. Balachandran and S. Vaidya, Spontaneous Lorentz violation in gauge theories, Eur. Phys. J. Plus 128 (2013) 118 [arXiv:1302.3406] [INSPIRE].
M. Henneaux, B. Julia and S. Silva, Noether superpotentials in supergravities, Nucl. Phys. B 563 (1999) 448 [hep-th/9904003] [INSPIRE].
C.W. Bunster, S. Cnockaert, M. Henneaux and R. Portugues, Monopoles for gravitation and for higher spin fields, Phys. Rev. D 73 (2006) 105014 [hep-th/0601222] [INSPIRE].
J.D. Brown and M. Henneaux, On the Poisson brackets of differentiable generators in classical field theory, J. Math. Phys. 27 (1986) 489 [INSPIRE].
A. Ashtekar and M. Streubel, Symplectic geometry of radiative modes and conserved quantities at null infinity, Proc. Roy. Soc. Lond. A 376 (1981) 585 [INSPIRE].
A. Ashtekar, Asymptotic quantization of the gravitational field, Phys. Rev. Lett. 46 (1981) 573 [INSPIRE].
A. Ashtekar, Asymptotic quantization: based on 1984 Naples lectures, Bibliopolis, Naples, Italy (1987).
A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP 05 (2015) 151 [arXiv:1401.7026] [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a new soft graviton theorem, arXiv:1404.4091 [INSPIRE].
A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
S. Pasterski, A. Strominger and A. Zhiboedov, New gravitational memories, JHEP 12 (2016) 053 [arXiv:1502.06120] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of gravity and soft theorems for massive particles, JHEP 12 (2015) 094 [arXiv:1509.01406] [INSPIRE].
E. Conde and P. Mao, BMS supertranslations and not so soft gravitons, JHEP 05 (2017) 060 [arXiv:1612.08294] [INSPIRE].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New symmetries of massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].
V. Lysov, S. Pasterski and A. Strominger, Low’s subleading soft theorem as a symmetry of QED, Phys. Rev. Lett. 113 (2014) 111601 [arXiv:1407.3814] [INSPIRE].
T. He, P. Mitra and A. Strominger, 2D Kac-Moody Symmetry of 4D Yang-Mills Theory, JHEP 10 (2016) 137 [arXiv:1503.02663] [INSPIRE].
D. Kapec, M. Pate and A. Strominger, New Symmetries of QED, Adv. Theor. Math. Phys. 21 (2017) 1769 [arXiv:1506.02906] [INSPIRE].
M. Campiglia and A. Laddha, Subleading soft photons and large gauge transformations, JHEP 11 (2016) 012 [arXiv:1605.09677] [INSPIRE].
E. Conde and P. Mao, Remarks on asymptotic symmetries and the subleading soft photon theorem, Phys. Rev. D 95 (2017) 021701 [arXiv:1605.09731] [INSPIRE].
M. Campiglia and R. Eyheralde, Asymptotic U(1) charges at spatial infinity, JHEP 11 (2017) 168 [arXiv:1703.07884] [INSPIRE].
A. Laddha and P. Mitra, Asymptotic symmetries and subleading soft photon theorem in effective field theories, JHEP 05 (2018) 132 [arXiv:1709.03850] [INSPIRE].
M. Herberthson and M. Ludvigsen, A relationship between future and past null infinity, Gen. Rel. Grav. 24 (1992) 1185.
D. Christodoulou and S. Klainerman, The global nonlinear stability of the Minkowski space, Princeton University Press, Princeton U.S.A. (1993).
L. Bieri, An extension of the stability theorem of the Minkowski space in general relativity, J. Diff. Geom. 86 (2010) 17 [arXiv:0904.0620] [INSPIRE].
H. Friedrich, Peeling or not peeling — Is that the question?, Class. Quant. Grav. 35 (2018) 083001 [arXiv:1709.07709] [INSPIRE].
P. Hintz and A. Vasy, A global analysis proof of the stability of Minkowski space and the polyhomogeneity of the metric, arXiv:1711.00195 [INSPIRE].
T.-T. Paetz, On the smoothness of the critical sets of the cylinder at spatial infinity in vacuum spacetimes, arXiv:1804.05034 [INSPIRE].
T. Banks, A Critique of pure string theory: heterodox opinions of diverse dimensions, hep-th/0306074 [INSPIRE].
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
G. Barnich and C. Troessaert, Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited, Phys. Rev. Lett. 105 (2010) 111103 [arXiv:0909.2617] [INSPIRE].
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Henneaux, M., Troessaert, C. Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity. J. High Energ. Phys. 2018, 171 (2018). https://doi.org/10.1007/JHEP07(2018)171
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DOI: https://doi.org/10.1007/JHEP07(2018)171