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.

27 pages; Dedicated to Rafael Sorkin on the occasion of his 60th birthday; v2 minor changes

References in corpus (1)

• The non-zero energy of 2+1 Minkowski space

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