Covariant Counterterms and Conserved Charges in Asymptotically Flat Spacetimes

TL;DR

This paper demonstrates that covariant boundary terms in gravitational actions lead to well-defined conserved charges in asymptotically flat spacetimes, aligning with ADM and Ashtekar-Hansen formalisms in various dimensions.

Contribution

It explicitly connects covariant counterterm methods to ADM and Ashtekar-Hansen formalisms, clarifying their equivalence in defining conserved charges.

Findings

Covariant boundary terms reproduce ADM action in higher dimensions.

Conserved charges from counter-term methods match Ashtekar-Hansen charges in 4D.

The approach provides a unified framework for conserved quantities in flat spacetimes.

Abstract

Recent work has shown that the addition of an appropriate covariant boundary term to the gravitational action yields a well-defined variational principle for asymptotically flat spacetimes and thus leads to a natural definition of conserved quantities at spatial infinity. Here we connect such results to other formalisms by showing explicitly i) that for spacetime dimension $d \ge 4$ the canonical form of the above-mentioned covariant action is precisely the ADM action, with the familiar ADM boundary terms and ii) that for $d=4$ the conserved quantities defined by counter-term methods agree precisely with the Ashtekar-Hansen conserved charges at spatial infinity.