Noether-Charge Realization of Diffeomorphism Algebra

TL;DR

This paper demonstrates that in general relativity, Noether charges associated with diffeomorphisms form a diffeomorphism algebra, and the central term vanishes on Killing horizons for many vector fields, using covariant phase space and null tetrads.

Contribution

It establishes the algebraic structure of Noether charges in general relativity and shows the absence of a central extension on Killing horizons for a broad class of vector fields.

Findings

Noether charges form a diffeomorphism algebra in general relativity.

The central term of the algebra vanishes on Killing horizons.

Null tetrads help analyze the algebra everywhere on the horizon.

Abstract

It is shown in the covariant phase space formalism that the Noether charges with respect to the diffeomorphism generated by vector fields and their horizontal variations in general relativity form a diffeomorphism algebra. It is also shown with the help of the null tetrad which is well defined everywhere that the central term of the reduced diffeomorphism algebra on the Killing horizon for a large class of vector fields vanishes.