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Aspects of Double Null Physics

par Tan, Wendi
Président du jury Argurio, Riccardo
Promoteur Barnich, Glenn
Publication Non publié, 2026-03-13

Thèse de doctorat

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Résumé :	This thesis is motivated by the aim of overcoming the asymmetric treatment of ingoing and outgoing radiation in the Bondi-Sachs and Newman-Unti frameworks, as well as by the development of a more natural and covariant approach to characteristic initial value problems in field theory and general relativity. To this end, we investigate several aspects of a new double-null framework.
	First, we analyze a free massless scalar field in two dimensions and construct a covariant Hamiltonian framework on a timelike cylinder, corresponding to two-dimensional Minkowski spacetime with periodic spatial boundary conditions. By choosing one or two null directions as evolution parameters, the theory is formulated directly on null slices, without relying on large-radius asymptotic expansions. We discuss the subtleties related to the dynamics, global and infinite-dimensional conformal symmetries, canonical quantization, and partition functions in both single and double light-front formulations. The equivalence with the instant form is then examined, with particular emphasis on matching conditions and the consistent treatment of zero modes. A brief extension to the massive case in two dimensions is also presented.
	Another central part of the thesis is devoted to the construction of a double-null gauge for three-dimensional pure Einstein gravity. This gauge, formulated within the Newman-Penrose formalism using global coordinates (u, v, phi), treats ingoing and outgoing radiation on an equal footing and may serve as a foundation for an approach to flat holography. We derive the solution space, analyze the associated phase space, and study the residual symmetries and the asymptotic structure under appropriate boundary conditions. The resulting asymptotic symmetry algebra is R^2 semidirect product Diff(S^1), analogous to BMS3, but without boost generators. Finally, we explore a link between past and future null infinity through the study of the angular deflection of photons.
	The thesis also provides a detailed presentation of the Newman-Penrose formalism and its applications to memory effects, together with a unified treatment of electromagnetic, gravitational, and dilaton memory effects in Einstein-Maxwell-dilaton theories.