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    Thermodynamic Volumes and Isoperimetric Inequalities for de Sitter Black Holes


    Dolan, Brian P. and Kastor, David and Kubiznak, David and Mann, Robert B. and Traschen, Jennie (2012) Thermodynamic Volumes and Isoperimetric Inequalities for de Sitter Black Holes. Working Paper. Dublin Institute for Advanced Studies DIAS-STP-13-01.

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    Abstract

    We consider the thermodynamics of rotating and charged asymptotically de Sitter black holes. Using Hamiltonian perturbation theory techniques, we derive three different first law relations including variations in the cosmological constant, and associated Smarr formulas that are satisfied by such spacetimes. Each first law introduces a different thermodynamic volume conjugate to the cosmological constant. We examine the relation between these thermodynamic volumes and associated geometric volumes in a number of examples, including Kerr-dS black holes in all dimensions and Kerr-Newman-dS black holes in D = 4. We also show that the Chong-Cvetic-Lu-Pope solution of D = 5 minimal supergravity, analytically continued to positive cosmological constant, describes black hole solutions of the Einstein-Chern-Simons theory and include such charged asymptotically de Sitter black holes in our analysis. In all these examples we find that the particular thermodynamic volume associated with the region between the black hole and cosmological horizons is equal to the naive geometric volume. Isoperimetric inequalities, which hold in the examples considered, are formulated for the different thermodynamic volumes and conjectured to remain valid for all asymptotically de Sitter black holes. In particular, in all examples considered, we find that for fixed volume of the observable universe, the entropy is increased by adding black holes. We conjecture that this is true in general.

    Item Type: Monograph (Working Paper)
    Additional Information: We would like to thank Mirjam Cvetic for helpful discussions, Gary W. Gibbons for useful comments and reading the manuscript, and the anonymous referee for suggesting we investigate the Nariai limit. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (Mann) and was supported in part by NSF grant PHY-0555304 (Kastor and Traschen). Kastor, Kubiznak, and Traschen thank the Benasque Center for Theoretical Physics, at which this work was started, for their hospitality. Traschen thanks the Perimeter Institute, at which this work was mostly completed, for their hospitality.
    Keywords: Thermodynamic Volumes; Isoperimetric Inequalities; de Sitter Black Holes;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 4446
    Depositing User: Dr. Brian Dolan
    Date Deposited: 03 Sep 2013 13:25
    Publisher: Dublin Institute for Advanced Studies DIAS-STP-13-01
    URI:

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