Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity

TL;DR

This paper develops new asymptotic conditions for the Einstein-Maxwell system at spatial infinity, revealing a richer symmetry structure and explicit Hamiltonian charges, with implications for null infinity matching.

Contribution

It introduces a novel set of asymptotic conditions that include magnetic solutions and extend the BMS algebra to Einstein-Maxwell systems with explicit charge generators.

Findings

Inclusion of magnetic solutions in asymptotic conditions.

Extended BMS algebra with electromagnetic symmetries.

Explicit form of Hamiltonian charge-generators.

Abstract

We present a new set of asymptotic conditions for gravity at spatial infinity that includes gravitational magnetic-type solutions, allows for a non-trivial Hamiltonian action of the complete $BMS_4$ algebra, and leads to a non-divergent behaviour of the Weyl tensor as one approaches null infinity. We then extend the analysis to the coupled Einstein-Maxwell system and obtain as canonically realized asymptotic symmetry algebra a semi-direct sum of the $BMS_4$ algebra with the angle dependent $u(1)$ transformations. The Hamiltonian charge-generator associated with each asymptotic symmetry element is explicitly written. The connection with matching conditions at null infinity is also discussed.