Geometric invariance of mass-like asymptotic invariants

TL;DR

This paper investigates the coordinate-invariance of asymptotic invariants like ADM mass, providing a conceptual explanation for the cancellation of certain divergent terms under coordinate changes at infinity.

Contribution

It offers a theoretical understanding of why certain asymptotic invariants remain invariant under coordinate transformations, clarifying a previously observed cancellation phenomenon.

Findings

Identifies divergence terms that cancel out in the invariance proof

Provides a conceptual framework for understanding coordinate invariance

Clarifies the geometric nature of mass-like asymptotic invariants

Abstract

We study coordinate-invariance of some asymptotic invariants such as the ADM mass or the Chru\'sciel-Herzlich momentum, given by an integral over a "boundary at infinity". When changing the coordinates at infinity, some terms in the change of integrand do not decay fast enough to have a vanishing integral at infinity; but they may be gathered in a divergence, thus having vanishing integral over any closed hypersurface. This fact could only be checked after direct calculation (and was called a "curious cancellation"). We give a conceptual explanation thereof.