Thermodynamic Volumes and Isoperimetric Inequalities for de Sitter Black Holes
By Brian P. Dolan, David Kastor, D. Kubizňák, Robert B. Mann, Jennie Traschen. 2013
271 citations recorded by the source corpus.
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.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/66cd7cfc341951f8bcb88a7d20e589a4afd39dbd
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Citations in the corpus
- Black hole chemistry: thermodynamics with Lambda (2016, background): “7) and for standard examples equals the naive geometric volume [50].”
- On the critical phenomena and thermodynamics of charged topological dilaton AdS black holes (2013, methodology): “ions of d-dimensional charged GB-AdS black hole agree with the (P ∼ V)ones in van der Waals vapor-liquid system. Recently, many interests focus on the studies of critical behaviors of AdS black holes [36, 37, 38, 39]by considering cosmological constant as thermal pressure P = − 1 8π Λ = 3 8π 1 l2 , ”
- Thermodynamics of Rotating Black Holes and Black Rings: Phase Transitions and Thermodynamic Volume (2014, background): “Extensions of this idea to asymptotically de Sitter space times have also been recently explored, with the resultant thermodynamic notions for black holes remaining intact [41] (see also [42–50]).”
- Multiple reentrant phase transitions and triple points in Lovelock thermodynamics (2014, background): “This proposal has been shown to provide a much richer panoply of thermodynamic behaviour for both AdS and dS black holes [19].”