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.

50 pages, 1 figure. v2: added references and a paragraph in the conclusion on supersymmetric extensions

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Cited by in corpus (4)

• The partial Bondi gauge: Gauge fixings and asymptotic charges
• Symmetries of the gravitational scattering in the absence of peeling
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• Robinson-Trautman spacetimes in (2+1) dimensions