Three-dimensional asymptotically flat Einstein-Maxwell theory

TL;DR

This paper solves the 3D Einstein-Maxwell theory with non-trivial null infinity asymptotics, revealing a Virasoro-Kac-Moody symmetry algebra and complex solution space features, including non-conserved charges influenced by electromagnetic news.

Contribution

It introduces a detailed solution space for 3D Einstein-Maxwell theory with asymptotic analysis and identifies the extended symmetry algebra.

Findings

Symmetry algebra is a Virasoro-Kac-Moody type extending bms3.

Solution space includes logarithmic and polyhomogeneous solutions.

Surface charges are non-integrable and non-conserved due to electromagnetic news.

Abstract

Three-dimensional Einstein-Maxwell theory with non trivial asymptotics at null infinity is solved. The symmetry algebra is a Virasoro-Kac-Moody type algebra that extends the bms3 algebra of the purely gravitational case. Solution space involves logarithms and provides a tractable example of a polyhomogeneous solution space. The associated surface charges are non-integrable and non-conserved due to the presence of electromagnetic news. As in the four dimensional purely gravitational case, their algebra involves a field-dependent central charge.