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Infrared Symmetries of General Relativity

Lecturer

Níckolas de Aguiar Alves (UFABC, Brazil)

Language

English

Schedule

15–19 Jul 2024 (5 classes, mandatory attendance in 4 for a certificate)

Time

16h00 (BRT)/19h00 (UTC)

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

Prerequisites

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.

• Robert M. Wald. General Relativity (University of Chicago Press: Chicago, IL, 1984).
• Stephen W. Hawking and George F. R. Ellis. The Large Scale Structure of Spacetime (Cambridge University Press: Cambridge, 1973).
• Roger Penrose. “Asymptotic Properties of Fields and Space-Times”. Physical Review Letters 10 (2), 66–68 (1963).
• C. Duval, G. W. Gibbons, P. A. Horvathy, and P. M. Zhang. “Carroll versus Newton and Galilei”. Classical and Quantum Gravity 31 (8), 085016 (2014). arXiv: 1402.0657 [gr-qc].
• C. Duval, G. W. Gibbons, and P. A. Horvathy. “Conformal Carrol groups and BMS symmetry”. Classical and Quantum Gravity 31 (9), 092001 (2014). arXiv: 1402.5894 [gr-qc].
• Claudio Dappiaggi, Valter Moretti, and Nicola Pinamonti. Hadamard States From Light-like Hypersurfaces (Springer: Cham, 2017). arXiv: 1706.09666 [math-ph].
• Andrew Strominger. Lectures on the Infrared Structure of Gravity and Gauge Theory (Princeton University Press: Princeton, NJ, 2018). arXiv: 1703.05448 [hep-th].

Resources

• Lecture notes (original version)
• Níckolas de Aguiar Alves. “Lectures on the Bondi–Metzner–Sachs group and related topics in infrared physics”. The European Physical Journal C (2026). arXiv: 2504.12521 [gr-qc]. Forthcoming.

Recordings