Superboost transitions, refraction memory and super-Lorentz charge algebra
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.
KeywordsClassical Theories of Gravity Gauge Symmetry Space-Time Symmetries
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.
- 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].
- S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].  Y.B. Zel’dovich and A.G. Polnarev, Radiation of gravitational waves by a cluster of superdense stars, Sov. Astron. 18 (1974) 17.
- 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.Google Scholar
- 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.Google Scholar
- Y. Nutku and R. Penrose, On Impulsive Gravitational Waves, Twistor Newslett. 34 (1992) 9.Google Scholar
- D. Christodoulou and S. Klainerman, The Global nonlinear stability of the Minkowski space, Princeton University Press (1993) [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. Geroch, Asymptotic Structure of Space-Time, in Asymptotic Structure of Space-Time, F.P. Esposito and L. Witten eds., Springer (1977), pg. 1.Google Scholar