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Finite BMS transformations

Glenn Barnich, Cédric Troessaert

TL;DR

The paper develops a systematic framework for finite BMS and Weyl transformations acting on gravitational data at Scri in three and four dimensions, allowing for an arbitrary boundary conformal factor. It combines adapted Cartan and Newman-Penrose formalisms to derive how asymptotic solution spaces transform under the full symmetry groups, including the Schwarzian-type structures in AdS3 and the extended BMS4 group with complex rescalings in NU and NP formalisms. Key results include explicit transformation laws for boundary data, mass and angular momentum aspects, and Weyl-invariant contents of the solution space, providing a basis for Ward identities and memory-effect analyses in both AdS and flat settings. The work sets the stage for deeper physical applications of asymptotic symmetries, such as constraints on scattering and memory phenomena, across different spacetime dimensions and topologies.

Abstract

The action of finite BMS and Weyl transformations on the gravitational data at null infinity is worked out in three and four dimensions in the case of an arbitrary conformal factor for the boundary metric induced on Scri.

Finite BMS transformations

TL;DR

The paper develops a systematic framework for finite BMS and Weyl transformations acting on gravitational data at Scri in three and four dimensions, allowing for an arbitrary boundary conformal factor. It combines adapted Cartan and Newman-Penrose formalisms to derive how asymptotic solution spaces transform under the full symmetry groups, including the Schwarzian-type structures in AdS3 and the extended BMS4 group with complex rescalings in NU and NP formalisms. Key results include explicit transformation laws for boundary data, mass and angular momentum aspects, and Weyl-invariant contents of the solution space, providing a basis for Ward identities and memory-effect analyses in both AdS and flat settings. The work sets the stage for deeper physical applications of asymptotic symmetries, such as constraints on scattering and memory phenomena, across different spacetime dimensions and topologies.

Abstract

The action of finite BMS and Weyl transformations on the gravitational data at null infinity is worked out in three and four dimensions in the case of an arbitrary conformal factor for the boundary metric induced on Scri.

Paper Structure

This paper contains 21 sections, 233 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Adapted Cartan formulation
  3. Newman-Penrose formalism in 3d
  4. 3d asymptotically AdS spacetimes at spatial infinity
  5. Fefferman-Graham solution space
  6. Residual gauge symmetries
  7. Action of conformal and Weyl group
  8. 3d asymptotically flat spacetimes at null infinity
  9. Solution space
  10. Residual gauge symmetries
  11. Combined BMS3 and Weyl group
  12. Action on solution space
  13. 4d asymptotically flat spacetimes at null infinity
  14. Newman-Penrose formalism in 4d
  15. Newman-Unti solution space
  16. ...and 6 more sections