Abstract
The Bondi-van der Burg-Metzner-Sachs (BMS) group is the asymptotic symmetry group of asymptotically flat spacetime. It is infinite dimensional and entails an infinite number of conservation laws. According to the black hole membrane paradigm, null infinity (in asymptotically flat spacetime) and black hole event horizons behave like fluid membranes. The fluid dynamics of the membrane is governed by an infinite set of symmetries and conservation laws. Our main result is to point out that the infinite set of symmetries and conserved charges of the BMS group and the membrane paradigm are the same. This relationship has several consequences. First, it sheds light on the physical interpretation of BMS conservation laws. Second, it generalizes the BMS conservation laws to arbitrary subregions of arbitrary null surfaces. Third, it clarifies the identification of the superrotation subgroup of the BMS group. We briefly comment on the black hole information problem.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Bondi, M.G.J. van der Burg and A.W.K. Metzner, Gravitational waves in general relativity. VII. Waves from axi-symmetric isolated systems, Roy. Soc. London Proc. A 269 (1962) 21.
R.K. Sachs, Gravitational Waves in General Relativity. VIII. Waves in asymptotically flat space-time, Roy. Soc. London Proc. A 270 (1962) 103.
J. de Boer and S.N. Solodukhin, A holographic reduction of Minkowski space-time, Nucl. Phys. B 665 (2003) 545 [hep-th/0303006] [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].
G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
G. Barnich and C. Troessaert, Supertranslations call for superrotations, PoS(CNCFG2010)010 [arXiv:1102.4632] [INSPIRE].
A. Strominger, On BMS invariance of gravitational scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028 [arXiv:1408.2228] [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a new soft graviton theorem, arXiv:1404.4091 [INSPIRE].
M. Campiglia and A. Laddha, New symmetries for the gravitational S-matrix, JHEP 04 (2015) 076 [arXiv:1502.02318] [INSPIRE].
D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Higher-dimensional supertranslations and Weinberg’s soft graviton theorem, arXiv:1502.07644 [INSPIRE].
S. Pasterski, A. Strominger and A. Zhiboedov, New gravitational memories, arXiv:1502.06120 [INSPIRE].
A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
S.W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].
G. ’t Hooft, Black holes, Hawking radiation and the information paradox, Nucl. Phys. Proc. Suppl. 43 (1995) 1 [INSPIRE].
G. ’t Hooft, The scattering matrix approach for the quantum black hole: An Overview, Int. J. Mod. Phys. A 11 (1996) 4623 [gr-qc/9607022] [INSPIRE].
J. Polchinski, Chaos in the black hole S-matrix, arXiv:1505.08108 [INSPIRE].
G.t. Hooft, Diagonalizing the black hole information retrieval process, arXiv:1509.01695 [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Soft hair on black holes, arXiv:1601.00921 [INSPIRE].
T. Damour, Quelques proprietes mecaniques, electromagnet iques, thermodynamiques et quantiques des trous noir, Ph.D. thesis, Paris University, Paris, France (1979).
T. Damour, Surface effects in black-hole physics, in Marcel Grossmann Meeting: general relativity, R. Ruffini ed., North-Holland Publishing Company (1982).
R.H. Price and K.S. Thorne, Membrane viewpoint on black holes: properties and evolution of the stretched horizon, Phys. Rev. D 33 (1986) 915 [INSPIRE].
K.S. Thorne, R.H. Price and D.A. MacDonald, Black holes: the membrane paradigm, Yale University Press, U.S.A. (1986).
M. Parikh and F. Wilczek, An action for black hole membranes, Phys. Rev. D 58 (1998) 064011 [gr-qc/9712077] [INSPIRE].
R.F. Penna, Energy extraction from boosted black holes: Penrose process, jets and the membrane at infinity, Phys. Rev. D 91 (2015) 084044 [arXiv:1503.00728] [INSPIRE].
A. Balachandran, A. Momen and L. Chandar, Edge states in gravity and black hole physics, Nucl. Phys. B 461 (1996) 581.
L. Donnay, G. Giribet, H.A. Gonzalez and M. Pino, Super-translations and super-rotations at the horizon, arXiv:1511.08687 [INSPIRE].
E.E. Flanagan and D.A. Nichols, Conserved charges of the extended Bondi-Metzner-Sachs algebra, arXiv:1510.03386 [INSPIRE].
G. Barnich and C. Troessaert, BMS charge algebra, JHEP 12 (2011) 105 [arXiv:1106.0213] [INSPIRE].
G.T. Horowitz and J.M. Maldacena, The black hole final state, JHEP 02 (2004) 008 [hep-th/0310281] [INSPIRE].
R. Penrose and W. Rindler, Spinors and space-time, Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge U.K. (2011).
D. Kapec, M. Pate and A. Strominger, New symmetries of QED, arXiv:1506.02906 [INSPIRE].
E. Poisson, A relativist’s toolkit: the mathematics of black-hole mechanics, Cambridge University Press, Cambridge U.K. (2004).
D. Kapec, V. Lysov and A. Strominger, Asymptotic symmetries of massless QED in even dimensions, arXiv:1412.2763 [INSPIRE].
T. He, P. Mitra and A. Strominger, 2D Kac-Moody symmetry of 4D Yang-Mills theory, arXiv:1503.02663 [INSPIRE].
S. Pasterski, Asymptotic Symmetries and Electromagnetic Memory, arXiv:1505.00716 [INSPIRE].
L. Susskind, Electromagnetic memory, arXiv:1507.02584 [INSPIRE].
S. Dubovsky, L. Hui, A. Nicolis and D.T. Son, Effective field theory for hydrodynamics: thermodynamics and the derivative expansion, Phys. Rev. D 85 (2012) 085029 [arXiv:1107.0731] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1508.06577
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Penna, R.F. BMS invariance and the membrane paradigm. J. High Energ. Phys. 2016, 23 (2016). https://doi.org/10.1007/JHEP03(2016)023
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2016)023