TL;DR
This paper constructs surface charges for asymptotic symmetries in four-dimensional flat spacetimes, revealing a field-dependent central extension that affects the BMS algebra and diverges in certain cases like Kerr black holes.
Contribution
It introduces a detailed construction of surface charges with a generalized cocycle condition, highlighting the role of field-dependent central extensions in the BMS algebra.
Findings
Central extension vanishes for globally well-defined BMS algebra.
Supertranslation charges diverge for Kerr black hole.
Superrotation charges remain finite with no divergences.
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.
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