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

TL;DR

This paper reexamines the phase space reduction of Schwarzschild black holes considering asymptotically nontrivial gauge transformations, revealing superselection rules for ADM mass and analyzing variational principles with phenomenological clocks.

Contribution

It introduces a new perspective on gauge freedom in black hole phase space reduction, highlighting superselection rules and the role of clocks at asymptotic boundaries.

Findings

Superselection rules for ADM mass are established.

Additional gauge transformations correspond to asymptotically nontrivial diffeomorphisms.

Phenomenological clocks influence variational principles at boundaries.

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}.