Conformal symmetries of gravity from asymptotic methods: further developments
Pierre-Henry Lambert
TL;DR
The thesis demonstrates a robust enhancement of gravitational symmetry at null infinity beyond the classic BMS structure. It shows that Virasoro-type extensions arise not only in AdS/CFT settings but also for asymptotically flat spacetimes in Newman–Unti gauge, with conformal data playing a central role; transformation laws for Newman–Penrose coefficients reveal central extensions and a field-dependent charge algebra. Extending the analysis to Einstein–Yang–Mills in $d$ dimensions, it confirms a Virasoro–Kac–Moody type algebra in both 3D and 4D asymptotically flat cases, and provides a unified treatment of the gauge structure, fall-offs, and charges. In parallel, the work derives detailed solution spaces and surface-charge algebras for Einstein–Maxwell systems in 3D and 4D, highlighting how radiation data (news) governs mass and angular momentum evolution and how holographic currents and central extensions emerge in the asymptotic symmetry framework. Collectively, these results deepen the understanding of gravity’s boundary symmetries and their holographic and soft-theorem implications, with explicit mappings between gauges and clear prescriptions for charges and their algebras across dimensions and cosmological constants.
Abstract
In this thesis, the symmetry structure of gravitational theories at null infinity is studied further, in the case of pure gravity in four dimensions and also in the case of Einstein-Yang-Mills theory in $d$ dimensions with and without a cosmological constant. The first part of this thesis is devoted to the presentation of asymptotic methods (symmetries, solution space and surface charges) applied to gravity in the case of the BMS gauge in three and four spacetime dimensions. The second part of this thesis contains the original contributions. Firstly, it is shown that the enhancement from Lorentz to Virasoro algebra also occurs for asymptotically flat spacetimes defined in the sense of Newman-Unti. As a first application, the transformation laws of the Newman-Penrose coefficients characterizing solution space of the Newman-Unti approach are worked out, focusing on the inhomogeneous terms that contain the information about central extensions of the theory. These transformations laws make the conformal structure particularly transparent, and constitute the main original result of the thesis. Secondly, asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner in $d$ dimensions. In agreement with a recent conjecture, a Virasoro-Kac-Moody type algebra is found not only in three dimensions but also in the four dimensional asymptotically flat case. These two parts of the thesis are supplemented by appendices.