Lie Theory for Asymptotic Symmetries in General Relativity: The NU Group

Abstract

We study the Newman--Unti (NU) group from the viewpoint of infinite-dimensional geometry. The NU group is a topological group in a natural coarse topology, but it does not become a manifold and hence a Lie group in this topology. To obtain a manifold structure we consider a finer Whitney-type topology. This turns the unit component of the NU group into an infinite-dimensional Lie group. We then study the Lie theoretic properties of this group. Surprisingly, the group operations of the full NU group become discontinuous, whence the NU group does not support a Lie group structure. The NU group contains the Bondi--Metzner--Sachs (BMS) group as a subgroup, whose Lie group structure was constructed in a previous article. It is well known that the NU Lie algebra splits into a direct sum of Lie ideals of the Lie algebras of the BMS group and conformal rescalings of scri. However, the lack of a Lie group structure on the NU group implies that the BMS group cannot be embedded as a Lie subgroup therein.

37 pages, article; minor revisions; version to appear in Classical and Quantum Gravity

References in corpus (5)

• Asymptotic symmetries and subleading soft graviton theorem
• An introduction to infinite-dimensional differential geometry
• On the Various Extensions of the BMS Group
• Lie Theory for Asymptotic Symmetries in General Relativity: The BMS Group
• Differentiable vectors and unitary representations of Frechet-Lie supergroups

Cited by in corpus (6)

• Lie Theory for Asymptotic Symmetries in General Relativity: The BMS Group
• Using thermodynamics to learn gravitational wave physics
• Null infinity as a Killing horizon
• Group Contractions via Infinite-Dimensional Lie Theory
• Lectures on the Bondi--Metzner--Sachs group and related topics in infrared physics
• On the unit component of the Newman-Unti group