(Anti)-de Sitter with leaky boundaries and corners

TL;DR

This paper develops a framework for defining finite, conserved and non-conserved charges in four-dimensional spacetimes with a cosmological constant, including boundary and corner contributions, expanding the understanding of boundary conditions in AdS and dS spaces.

Contribution

It introduces a method to construct finite charges with leaky boundaries and corner terms, and generalizes the variational principle for AdS$_4$ with arbitrary boundary data.

Findings

Finite charges are obtained for any boundary conditions.

New Weyl charge identified for conformal boundary conditions.

Ward identities reproduce evolution equations for mass and angular momentum.

Abstract

We construct charges for four-dimensional spacetimes with a non-vanishing cosmological constant, including charges that are not conserved because of a leaky boundary and charges associated with corner terms in the symplectic current. The construction leads to manifestly finite charges for any choice of boundary conditions, and reveals new charges in partial Bondi gauge for an enlarged class of field configurations which are not fully on-shell, including a Weyl charge for conformal boundary conditions. In addition, we generalize the variational principle for AdS$_4$ gravity with Dirichlet boundary conditions to a wedge of spacetime where the conformal boundary includes a corner. The boundary data is completely general, with no conditions restricting time dependence or the determinant of the metric. The Ward identities associated with boundary diffeomorphisms are shown to reproduce the evolution equations for the mass and angular momentum of fully on-shell field configurations.