The identification between the bulk and boundary conserved quantities

TL;DR

This paper demonstrates that the Wald formalism establishes a consistent identification between bulk and boundary conserved quantities in both asymptotically flat and AdS stationary spacetimes, extending previous results.

Contribution

It generalizes the bulk-boundary conserved quantity identification to asymptotically AdS spacetimes and clarifies its reduction to the test particle case.

Findings

Identification holds in asymptotically AdS stationary spacetimes.

Reduction to the test particle case is consistent with the general matter field scenario.

The Wald formalism effectively relates bulk and boundary conserved quantities.

Abstract

By using Wald formalism, we show that the identification between the bulk and boundary conserved quantities induced by the perturbation of generic non-electromagnetic matter field holds not only on top of the asymptotically flat stationary spacetimes but also on top of the asymptotically AdS stationary ones. We further show that such an identification reduces to the familiar form for the test point particle by viewing it as the limiting case of general matter.