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Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory

Jorrit Bosma, Marc Geiller, Sucheta Majumdar, Blagoje Oblak

Abstract

We study the null asymptotic structure of Einstein-Maxwell theory in three-dimensional (3D) spacetimes. Although devoid of bulk gravitational degrees of freedom, the system admits a massless photon and can therefore accommodate electromagnetic radiation. We derive fall-off conditions for the Maxwell field that contain both Coulombic and radiative modes with non-vanishing news. The latter produces non-integrability and fluxes in the asymptotic surface charges, and gives rise to a non-trivial 3D Bondi mass loss formula. The resulting solution space is thus analogous to a dimensional reduction of 4D pure gravity, with the role of gravitational radiation played by its electromagnetic cousin. We use this simplified setup to investigate choices of charge brackets in detail, and compute in particular the recently introduced Koszul bracket. When the latter is applied to Wald-Zoupas charges, which are conserved in the absence of news, it leads to the field-dependent central extension found earlier in [arXiv:1503.00856]. We also consider (Anti-)de Sitter asymptotics to further exhibit the analogy between this model and 4D gravity with leaky boundary conditions.

Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory

Abstract

We study the null asymptotic structure of Einstein-Maxwell theory in three-dimensional (3D) spacetimes. Although devoid of bulk gravitational degrees of freedom, the system admits a massless photon and can therefore accommodate electromagnetic radiation. We derive fall-off conditions for the Maxwell field that contain both Coulombic and radiative modes with non-vanishing news. The latter produces non-integrability and fluxes in the asymptotic surface charges, and gives rise to a non-trivial 3D Bondi mass loss formula. The resulting solution space is thus analogous to a dimensional reduction of 4D pure gravity, with the role of gravitational radiation played by its electromagnetic cousin. We use this simplified setup to investigate choices of charge brackets in detail, and compute in particular the recently introduced Koszul bracket. When the latter is applied to Wald-Zoupas charges, which are conserved in the absence of news, it leads to the field-dependent central extension found earlier in [arXiv:1503.00856]. We also consider (Anti-)de Sitter asymptotics to further exhibit the analogy between this model and 4D gravity with leaky boundary conditions.
Paper Structure (48 sections, 16 equations, 1 figure)

This paper contains 48 sections, 16 equations, 1 figure.

Table of Contents

  1. Introduction and summary
  2. Motivations.
  3. Outline and summary of results.
  4. Pure Maxwell theory in 3D
  5. Fall-offs in Bondi gauge
  6. Fall-offs.
  7. Equations of motion.
  8. Gauge-invariant fields.
  9. Electromagnetic memory
  10. Setup for Einstein--Maxwell theory
  11. Lagrangian and Noether currents
  12. Fall-offs and radiative solution space
  13. Fall-offs and gauge conditions.
  14. Bondi hierarchy of field equations.
  15. Solution space.
  16. ...and 33 more sections

Figures (1)

  • Figure 1: A Penrose diagram of 3D Minkowski spacetime, showing retarded Bondi coordinates $(r,u,\phi)$ along with light-cones centred at the origin. Future null infinity is the region denoted $\mathscr{I}^+$, where $r\to\infty$ at finite $(u,\phi)$. The presence of electromagnetic radiation (wiggly lines) reaching $\mathscr{I}^+$ is diagnosed by a non-zero news function \ref{['NEWS']}. Adapted from Bekaert:2022ipg.