Conserved charges in asymptotically de Sitter spacetimes

TL;DR

The paper develops a covariant phase space framework to define Ashtekar–Bonga–Kesavan (ABK) charges for asymptotically de Sitter spacetimes under Dirichlet boundary conditions and proves these charges coincide with ABK’s construction. It then elucidates the relation between ABK charges and alternative notions, showing the counterterm charges differ by a constant, boundary-data–determined offset and that Kelly–Marolf charges agree with ABK charges in their overlapping regime. The authors provide explicit Fefferman–Graham representations of Schwarzschild–de Sitter (and related) solutions in four and five dimensions to test the formalism and demonstrate consistency with the Weyl tensor’s electric part as used by ABK. Overall, the work clarifies the landscape of de Sitter charges and offers a concrete, covariant method for comparing different approaches in a unified framework.

Abstract

We present a covariant phase space construction of hamiltonian generators of asymptotic symmetries with `Dirichlet' boundary conditions in de Sitter spacetime, extending a previous study of Jäger. We show that the de Sitter charges so defined are identical to those of Ashtekar, Bonga, and Kesavan (ABK). We then present a comparison of ABK charges with other notions of de Sitter charges. We compare ABK charges with counterterm charges, showing that they differ only by a constant offset, which is determined in terms of the boundary metric alone. We also compare ABK charges with charges defined by Kelly and Marolf at spatial infinity of de sitter spacetime. When the formalisms can be compared, we show that the two definitions agree. Finally, we express Kerr-de Sitter metrics in four and five dimensions in an appropriate Fefferman-Graham form.

Figures (1)

• Figure 1: Hypersurfaces $\Sigma_1$ and $\Sigma_2$ together with the portion ${\cal I}^+_{12}$ of ${\cal I}^+$ enclosing the spacetime volume $\Sigma_{12}$.