Covariant Counterterms and Conserved Charges in Asymptotically 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.