2013/01/31 by Brian P. Dolan, David Kastor, David Kubiznak +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.87.104017
13 pages, no figures v2:includes comments on the Nariai limit and compressibility of the black hole horizon, added references
arxiv created 2013/05/01 · openalex publication_date 2013/05/15 · arxiv updated 2013/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the thermodynamics of rotating and charged asymptotically de Sitter (dS) 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 a fixed volume of the observable universe, the entropy is increased by adding black holes. We conjecture that this is true in general.