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Infrared Symmetries of General Relativity

Lecturer: Níckolas de Aguiar Alves, MSc (UFABC)

Schedule: July 15 to July 19 (5 classes), all at 16h00 (BRT)/19h00 (UTC). One must attend at least 4 classes to receive a certificate.

Workload: 10h

Topics: Symmetries and groups in fundamental physics. Lorentz and Poincaré groups. Maps between manifolds and diffeomorphisms. Lie derivative. Conformal infinity in Minkowski spacetime. Asymptotically flat spacetimes. Carrollian structure of conformal infinity. Symmetries of conformal infinity and the BMS group. Applications.

Pre-requisites: A standard introductory course in general relativity.

Bibliography:

These are the main references for the course. A complete list of references is available in the lecture notes.

  1. Robert M. Wald. General Relativity. Chicago: The University of Chicago Press, 1984.
  2. Stephen W. Hawking e George F. R. Ellis. The Large Scale Structure of Spacetime. Cambridge Monographs on Mathematical Physics. Cambridge: Cambridge University Press, 1973.
  3. Roger Penrose. “Asymptotic Properties of Fields and Space-Times”. Physical Review Letters 10.2 (1963), pp. 66–68.
  4. C. Duval et al. “Carroll versus Newton and Galilei: Two Dual Non-Einsteinian Concepts of Time”. Classical and Quantum Gravity 31.8, 085016 (2014). arXiv: 1402.0657 [gr-qc].
  5. C. Duval, G. W. Gibbons e P. A. Horvathy. “Conformal Carroll Groups and BMS Symmetry”. Classical and Quantum Gravity 31.9, 092001 (2014). arXiv: 1402.5894 [gr-qc].
  6. Claudio Dappiaggi, Valter Moretti e Nicola Pinamonti. Hadamard States From Light-like Hypersurfaces. SpringerBriefs in Mathematical Physics 25. Cham: Springer, 2017. arXiv: 1706.09666 [math-ph].
  7. Andrew Strominger. Lectures on the Infrared Structure of Gravity and Gauge Theory. Princeton: Princeton University Press, 2018. arXiv: 1703.05448 [hep-th].