Conserved charges in asymptotically de Sitter spacetimes

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.

arXiv comment42 pages, 1 figure; v2: Version includes new references and comments; v3: accepted to CQG

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• The partial Bondi gauge: Gauge fixings and asymptotic charges
• Gravitational radiation condition at infinity with a positive cosmological constant
• Asymptotic Structure with a positive cosmological constant
• Hamiltonian charges in the asymptotically de Sitter spacetimes
• Charges, conserved quantities and fluxes in de Sitter spacetime
• Field-dependent diffeomorphisms and the transformation of surface charges between gauges
• The Kerr-de Sitter spacetime in Bondi coordinates