Mass Superselection, Canonical Gauge Transformations, and Asymptotically Flat Variational Principles

Abstract

The phase space reduction of Schwarzschild black holes by Thiemann and Kastrup and by Kucha\v{r} is reexamined from a different perspective on gauge freedom. This perspective introduces additional gauge transformations which correspond to asymptotically nontrivial diffeomorphisms. Various subtleties concerning variational principles for asymptotically flat systems are addressed which allow us to avoid the usual conclusion that treating such transformations as gauge implies the vanishing of corresponding total charges. Instead, superselection rules are found for the (nonvanishing) ADM mass at the asymptotic boundaries. The addition of phenomenological clocks at each asymptotic boundary is also studied and compared with the `parametrization clocks' of Kucha\v{r}.