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

TL;DR

The paper introduces a refined set of parity-based boundary conditions at spatial infinity that, unlike previous formulations, accommodate gravitational magnetic-type solutions and yield a finite symplectic form while realizing the full $BMS_4$ algebra via canonical charges. Extending to the Einstein-Maxwell system, the authors obtain a semi-direct product of $BMS_4$ with angle-dependent $u(1)$ transformations, with all generators having well-defined charges and no central extension. The work also clarifies the connection to matching conditions at null infinity, reinforcing the equivalence of the asymptotic symmetry structure at spatial and null infinity. These results provide a robust Hamiltonian framework for infrared aspects of gravity and electromagnetism and bode well for a Hamiltonian understanding of soft theorems.

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.