Towards the quasi-localization of canonical GR

TL;DR

This paper develops a systematic framework for quasi-localizing canonical general relativity, emphasizing gauge invariance of boundary terms and deriving conditions on generator vector fields and boundary volume forms.

Contribution

It introduces a new approach ensuring gauge invariance of boundary terms in the quasi-localization of canonical GR, with specific geometric conditions derived.

Findings

Generator vector fields must be divergence free with respect to a Sen-type connection.

The boundary volume form must be fixed from the spatial metric.

A systematic framework for quasi-localization of canonical GR is established.

Abstract

A general framework for a systematic quasi-localization of canonical general relativity and a new ingredient, the requirement of the gauge invariance of the boundary terms appearing in the calculation of Poisson brackets, are given. As a consequence of this it is shown, in particular, that the generator vector fields (built from the lapse and shift) of the quasi-local quantities must be divergence free with respect to a Sen-type connection; and the volume form induced from the spatial metric on the boundary surface must be fixed.