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Galaxies 2014, 2(1), 89-159; doi:10.3390/galaxies2010089

Thermodynamics of Rotating Black Holes and Black Rings: Phase Transitions and Thermodynamic Volume

Perimeter Institute, 31 Caroline St. N., Waterloo, ON N2L 2Y5, Canada
Facultad de Matemática, Astronomía y Física, FaMAF, Universidad Nacional de Córdoba, Instituto de Física Enrique Gaviola, IFEG, CONICET, Ciudad Universitaria, Córdoba 5000, Argentina
Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran
Author to whom correspondence should be addressed.
Received: 9 January 2014 / Revised: 6 February 2014 / Accepted: 7 February 2014 / Published: 3 March 2014
(This article belongs to the Special Issue Aspects of Black Hole Physics)


In this review we summarize, expand, and set in context recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. We specifically consider the thermodynamics of higher-dimensional rotating asymptotically flat and AdS black holes and black rings in a canonical (fixed angular momentum) ensemble. We plot the associated thermodynamic potential—the Gibbs free energy—and study its behavior to uncover possible thermodynamic phase transitions in these black hole spacetimes. We show that the multiply-rotating Kerr-AdS black holes exhibit a rich set of interesting thermodynamic phenomena analogous to the “every day thermodynamics” of simple substances, such as reentrant phase transitions of multicomponent liquids, multiple first-order solid/liquid/gas phase transitions, and liquid/gas phase transitions of the van derWaals type. Furthermore, the reentrant phase transitions also occur for multiply-spinning asymptotically flat Myers–Perry black holes. These phenomena do not require a variable cosmological constant, though they are more naturally understood in the context of the extended phase space. The thermodynamic volume, a quantity conjugate to the thermodynamic pressure, is studied for AdS black rings and demonstrated to satisfy the reverse isoperimetric inequality; this provides a first example of calculation confirming the validity of isoperimetric inequality conjecture for a black hole with non-spherical horizon topology. The equation of state P = P(V,T) is studied for various black holes both numerically and analytically—in the ultraspinning and slow rotation regimes.
Keywords: black holes; thermodynamics; gauge-gravity duality black holes; thermodynamics; gauge-gravity duality
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Altamirano, N.; Kubizňák, D.; Mann, R.B.; Sherkatghanad, Z. Thermodynamics of Rotating Black Holes and Black Rings: Phase Transitions and Thermodynamic Volume. Galaxies 2014, 2, 89-159.

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