The asymptotic structure of space-time (II)

The asymptotic structure of Einstein's theory is particularly rich, giving rise to infinite-dimensional symmetry algebras. The 2022-2023 lecture will be devoted to asymptotically flat spacetimes, where the symmetry algebra is the infinite-dimensional Bondi-Metzner-Sachs (BMS) algebra.

Questions addressed :

infinities in Minkowski space-time and the Penrose diagram
connection conditions between different infinities
asymptotic symmetries in electromagnetism
asymptotic symmetries in gravitation and the Bondi-Metzner-Sachs group
the problem of defining angular momentum and its solution
memory effect and asymptotic symmetries
ward identities and asymptotic symmetries - triangle infrared

The lectures will be supplemented by research seminars, close to the subject of the lecture and presenting a sample of the major challenges in the field.

General references for the lecture

Books

A. Strominger, "Lectures on the Infrared Structure of Gravity and Gauge Theory," Princeton University Press (2018) [arXiv:1703.05448[hep-th]].

R. M. Wald, "General Relativity," chapter 11, University of Chicago Press (1984)

Journal articles

F. Alessio and G. Esposito, "On the structure and applications of the Bondi-Metzner-Sachs group," Int. J. Geom. Meth. Mod. Phys. 15 (2018) no.02, 1830002 [arXiv:1709.05134[gr-qc]].

A. Ashtekar, M. Campiglia and A. Laddha, "Null infinity, the BMS group and infrared issues," Gen. Rel. Grav. 50 (2018) no.11, 140-163 [arXiv:1808.07093 [gr-qc]].

Research articles

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), 21-52.

R. K. Sachs, "Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times," Proc. Roy. Soc. Lond. A 270 (1962), 103-126.

R. Sachs, "Asymptotic symmetries in gravitational theory," Phys. Rev. 128 (1962) 2851.

R. Penrose, "Asymptotic properties of fields and space-times," Phys. Rev. Lett. 10 (1963) 66.

T. Regge and C. Teitelboim, "Role of Surface Integrals in the Hamiltonian Formulation of General Relativity," Annals Phys. 88 (1974) 286.

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.

R. Javadinezhad, U. Kol and M. Porrati, "Supertranslation-invariant dressed Lorentz charges," JHEP 04 (2022), 069 [arXiv:2202.03442 [hep-th]].

P. N. Chen, M. T. Wang, Y. K. Wang and S. T. Yau, "Supertranslation invariance of angular momentum," Adv. Theor. Math. Phys. 25 (2021) no.3, 777-789 [arXiv:2102.03235 [gr-qc]].

O. Fuentealba, M. Henneaux and C. Troessaert, "Logarithmic supertranslations and supertranslation-invariant Lorentz charges," JHEP 02 (2023) 248 [ arXiv:2211.10941 [hep-th]] (and references cited in this work)