Abstract
We derive a closed-form expression of the orbit of Minkowski spacetime under arbitrary Diff(S2) super-Lorentz transformations and supertranslations. Such vacua are labelled by the superboost, superrotation and supertranslation fields. Impulsive transitions among vacua are related to the refraction memory effect and the displacement memory effect. A phase space is defined whose asymptotic symmetry group consists of arbitrary Diff(S2) super-Lorentz transformations and supertranslations. It requires a renormalization of the symplectic structure. We show that our final surface charge expressions are consistent with the leading and subleading soft graviton theorems. We contrast the leading BMS triangle structure to the mixed overleading/subleading BMS square structure.
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. 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].
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].
A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
A. Strominger and A. Zhiboedov, Gravitational Memory, BMS Supertranslations and Soft Theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE]. [7] Y.B. Zel’dovich and A.G. Polnarev, Radiation of gravitational waves by a cluster of superdense stars, Sov. Astron. 18 (1974) 17.
D. Christodoulou, Nonlinear nature of gravitation and gravitational wave experiments, Phys. Rev. Lett. 67 (1991) 1486 [INSPIRE].
L. Blanchet and T. Damour, Tail Transported Temporal Correlations in the Dynamics of a Gravitating System, Phys. Rev. D 37 (1988) 1410 [INSPIRE].
L. Blanchet and T. Damour, Hereditary effects in gravitational radiation, Phys. Rev. D 46 (1992) 4304 [INSPIRE].
J. Frauendiener, Note on the memory effect, Class. Quant. Grav. 9 (1992) 1639.
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
G. Compère and A. Fiorucci, Advanced Lectures in General Relativity, arXiv:1801.07064 [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
D.A. Nichols, Center-of-mass angular momentum and memory effect in asymptotically flat spacetimes, Phys. Rev. D 98 (2018) 064032 [arXiv:1807.08767] [INSPIRE].
S. Pasterski, A. Strominger and A. Zhiboedov, New Gravitational Memories, JHEP 12 (2016) 053 [arXiv:1502.06120] [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].
M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90 (2014) 124028 [arXiv:1408.2228] [INSPIRE].
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, Aspects of the BMS/CFT correspondence, JHEP 05 (2010) 062 [arXiv:1001.1541] [INSPIRE].
G. Barnich and C. Troessaert, BMS charge algebra, JHEP 12 (2011) 105 [arXiv:1106.0213] [INSPIRE].
M. Campiglia and A. Laddha, New symmetries for the Gravitational S-matrix, JHEP 04 (2015) 076 [arXiv:1502.02318] [INSPIRE].
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].
T. Regge and C. Teitelboim, Role of Surface Integrals in the Hamiltonian Formulation of General Relativity, Annals Phys. 88 (1974) 286 [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
G. Barnich and F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys. B 633 (2002) 3 [hep-th/0111246] [INSPIRE].
G. Compere and D. Marolf, Setting the boundary free in AdS/CFT, Class. Quant. Grav. 25 (2008) 195014 [arXiv:0805.1902] [INSPIRE].
D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity S-matrix, JHEP 08 (2014) 058 [arXiv:1406.3312] [INSPIRE].
E. Conde and P. Mao, BMS Supertranslations and Not So Soft Gravitons, JHEP 05 (2017) 060 [arXiv:1612.08294] [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Superrotation Charge and Supertranslation Hair on Black Holes, JHEP 05 (2017) 161 [arXiv:1611.09175] [INSPIRE].
L. Blanchet and T. Damour, Radiative gravitational fields in general relativity I. general structure of the field outside the source, Phil. Trans. Roy. Soc. Lond. A 320 (1986) 379 [INSPIRE].
H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers and E. Herlt, Exact solutions of Einstein’s field equations, Cambridge University Press (2003) [INSPIRE].
R. Penrose, The geometry of impulsive gravitational waves, in General Relativity, Papers in Honour of J.L. Synge, Clarendon Press (1972), pg. 101.
Y. Nutku and R. Penrose, On Impulsive Gravitational Waves, Twistor Newslett. 34 (1992) 9.
J. Podolsky and J.B. Griffiths, Expanding impulsive gravitational waves, Class. Quant. Grav. 16 (1999) 2937 [gr-qc/9907022] [INSPIRE].
J.B. Griffiths, J. Podolsky and P. Docherty, An Interpretation of Robinson-Trautman type N solutions, Class. Quant. Grav. 19 (2002) 4649 [gr-qc/0208022] [INSPIRE].
J.B. Griffiths and P. Docherty, A Disintegrating cosmic string, Class. Quant. Grav. 19 (2002) L109 [gr-qc/0204085] [INSPIRE].
A. Strominger and A. Zhiboedov, Superrotations and Black Hole Pair Creation, Class. Quant. Grav. 34 (2017) 064002 [arXiv:1610.00639] [INSPIRE].
G. Compère and J. Long, Vacua of the gravitational field, JHEP 07 (2016) 137 [arXiv:1601.04958] [INSPIRE].
É. É. Flanagan and D.A. Nichols, Conserved charges of the extended Bondi-Metzner-Sachs algebra, Phys. Rev. D 95 (2017) 044002 [arXiv:1510.03386] [INSPIRE].
G. Compère and J. Long, Classical static final state of collapse with supertranslation memory, Class. Quant. Grav. 33 (2016) 195001 [arXiv:1602.05197] [INSPIRE].
J. Podolsky and R. Steinbauer, Geodesics in space-times with expanding impulsive gravitational waves, Phys. Rev. D 67 (2003) 064013 [gr-qc/0210007] [INSPIRE].
J. Podolsky and R. Svarc, Refraction of geodesics by impulsive spherical gravitational waves in constant-curvature spacetimes with a cosmological constant, Phys. Rev. D 81 (2010) 124035 [arXiv:1005.4613] [INSPIRE].
J. Podolsky, C. Sämann, R. Steinbauer and R. Svarc, The global uniqueness and C 1 -regularity of geodesics in expanding impulsive gravitational waves, Class. Quant. Grav. 33 (2016) 195010 [arXiv:1602.05020] [INSPIRE].
H. Bondi, Plane gravitational waves in general relativity, Nature 179 (1957) 1072 [INSPIRE].
P.M. Zhang, C. Duval, G.W. Gibbons and P.A. Horvathy, The Memory Effect for Plane Gravitational Waves, Phys. Lett. B 772 (2017) 743 [arXiv:1704.05997] [INSPIRE].
P.M. Zhang, C. Duval, G.W. Gibbons and P.A. Horvathy, Soft gravitons and the memory effect for plane gravitational waves, Phys. Rev. D 96 (2017) 064013 [arXiv:1705.01378] [INSPIRE].
P.M. Zhang, C. Duval, G.W. Gibbons and P.A. Horvathy, Velocity Memory Effect for Polarized Gravitational Waves, JCAP 05 (2018) 030 [arXiv:1802.09061] [INSPIRE].
P.M. Zhang, M. Elbistan, G.W. Gibbons and P.A. Horvathy, Sturm-Liouville and Carroll: at the heart of the memory effect, Gen. Rel. Grav. 50 (2018) 107 [arXiv:1803.09640] [INSPIRE].
J. Distler, R. Flauger and B. Horn, Double-soft graviton amplitudes and the extended BMS charge algebra, arXiv:1808.09965 [INSPIRE].
D. Christodoulou and S. Klainerman, The Global nonlinear stability of the Minkowski space, Princeton University Press (1993) [INSPIRE].
K. Parattu, S. Chakraborty, B.R. Majhi and T. Padmanabhan, A Boundary Term for the Gravitational Action with Null Boundaries, Gen. Rel. Grav. 48 (2016) 94 [arXiv:1501.01053] [INSPIRE].
L. Lehner, R.C. Myers, E. Poisson and R.D. Sorkin, Gravitational action with null boundaries, Phys. Rev. D 94 (2016) 084046 [arXiv:1609.00207] [INSPIRE].
W. Wieland, New boundary variables for classical and quantum gravity on a null surface, Class. Quant. Grav. 34 (2017) 215008 [arXiv:1704.07391] [INSPIRE].
C. Duval, G.W. Gibbons and P.A. Horvathy, Conformal Carroll groups and BMS symmetry, Class. Quant. Grav. 31 (2014) 092001 [arXiv:1402.5894] [INSPIRE].
P. Kraus, F. Larsen and R. Siebelink, The gravitational action in asymptotically AdS and flat space-times, Nucl. Phys. B 563 (1999) 259 [hep-th/9906127] [INSPIRE].
R.B. Mann and D. Marolf, Holographic renormalization of asymptotically flat spacetimes, Class. Quant. Grav. 23 (2006) 2927 [hep-th/0511096] [INSPIRE].
G. Barnich, F. Brandt and M. Henneaux, Local BRST cohomology in the antifield formalism. 1. General theorems, Commun. Math. Phys. 174 (1995) 57 [hep-th/9405109] [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].
A. Ashtekar, Geometry and Physics of Null Infinity, arXiv:1409.1800 [INSPIRE].
R. Geroch, Asymptotic Structure of Space-Time, in Asymptotic Structure of Space-Time, F.P. Esposito and L. Witten eds., Springer (1977), pg. 1.
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: 1810.00377
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Compère, G., Fiorucci, A. & Ruzziconi, R. Superboost transitions, refraction memory and super-Lorentz charge algebra. J. High Energ. Phys. 2018, 200 (2018). https://doi.org/10.1007/JHEP11(2018)200
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2018)200