Action, Mass and Entropy of Schwarzschild-de Sitter black holes and the de Sitter/CFT Correspondence

摘要

We investigate a recent proposal for defining a conserved mass inasymptotically de Sitter spacetimes that is based on a conjectured holographicduality between such spacetimes and Euclidean conformal field theory. We showthat an algorithm for deriving such terms in asymptotically anti de Sitterspacetimes has an asymptotically de Sitter counterpart, and derive the explicitform for such terms up to 9 dimensions. We show that divergences of theon-shell action for de Sitter spacetime are removed in any dimension ininflationary coordinates, but in covering coordinates a linear divergenceremains in odd dimensions that cannot be cancelled by local terms that arepolynomial in boundary curvature invariants. We show that the class ofSchwarzschild-de Sitter black holes up to 9 dimensions has finite action andconserved mass, and construct a definition of entropy outside the cosmologicalhorizon by generalizing the Gibbs-Duhem relation in asymptotically dSspacetimes. The entropy is agreement with that obtained from CFT methods in$d=2$. In general our results provide further supporting evidence for a dS/CFTcorrespondence, although some important interpretive problems remain.