BMS charge algebra

TL;DR

The paper constructs surface charges for the $\,\mathfrak{bms}_4$ asymptotic symmetry at null infinity and shows the charge algebra is realized up to a field-dependent central extension that obeys a generalized cocycle condition. This extension vanishes for the globally well-defined BMS algebra, but in the Kerr background with the extended algebra certain supertranslation charges diverge while the superrotation charges remain finite. The Kerr analysis yields a central term that is linear in the rotation parameter and involves divergent sphere integrals, raising questions about regularization and physical interpretation. The work highlights a non-standard extended conformal dual for four-dimensional asymptotically flat gravity and outlines potential paths for regularization and deeper holographic understanding, with connections to lower-dimensional BMS structures.

Abstract

The surface charges associated with the symmetries of asymptotically flat four dimensional spacetimes at null infinity are constructed. They realize the symmetry algebra in general only up to a field-dependent central extension that satisfies a suitably generalized cocycle condition. This extension vanishes when using the globally well defined BMS algebra. For the Kerr black hole and the enlarged BMS algebra with both supertranslations and superrotations, some of the supertranslations charges diverge whereas there are no divergences for the superrotation charges. The central extension is proportional to the rotation parameter and involves divergent integrals on the sphere.