Dolan, Brian P. and Kastor, David and Kubiznak, David and Mann, Robert B. and Traschen, Jennie (2013) Thermodynamic volumes and isoperimetric inequalities for de Sitter black holes. Physical Review D, 87 (104017). ISSN 1550-7998

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Abstract

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.

Item Type:	Article
Keywords:	Thermodynamic volumes; isoperimetric inequalities; de Sitter black holes
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	10483
Identification Number:	https://doi.org/10.1103/PhysRevD.87.104017
Depositing User:	Dr. Brian Dolan
Date Deposited:	14 Feb 2019 10:26
Journal or Publication Title:	Physical Review D
Publisher:	American Physical Society
Refereed:	Yes
URI:	https://journals.aps.org/prd/
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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