Mass and energy in general relativity
In this short note, the authors revisit the problem of how to assign a total mass to an asymptotically flat spacetime. To that end they refer to the standard definition of total mass in terms of asymptotically flat coordinates in which the spatial components of the metric take the form \[ g_{\mu\nu}= \delta_{\mu\nu}+ O(r^{- k}).\tag{\(*\)} \] They point out that for uniqueness of the total mass it is necessary to restrict to representations \((*)\) with \(k= 1\). Purely spatial coordinate transformations that lead to a representation \((*)\) with \(k\neq 1\) would lead to a different value for the total mass.
scientific article; zbMATH DE number 798684