Radiative asymptotic symmetries of 3D Einstein-Maxwell theory

Author:

Bosma Jorrit1,Geiller Marc2ORCID,Majumdar Sucheta2,Oblak Blagoje34ORCID

Affiliation:

1. Swiss Federal Institute of Technology in Zurich (ETH)

2. Laboratoire de Physique de l'ENS de Lyon

3. Université Libre de Bruxelles

4. Center of Theoretical Physics

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 [Class. Quantum Gravity 32, 245001 (2015)]. We also consider (Anti-)de Sitter asymptotics to further exhibit the analogy between this model and 4D gravity with leaky boundary conditions.

Funder

Agence Nationale de la Recherche

Fonds De La Recherche Scientifique - FNRS

Horizon 2020

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Publisher

Stichting SciPost

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