Notes on thermodynamics of super-entropic AdS black holes

Abstract

The super-entropic black hole, which possesses a noncompact horizon topology and violates the reverse isoperimetric inequality, has been found to satisfy both the thermodynamic first law and the Bekenstein-Smarr mass formula. In this paper, we first derive a new Christodoulou-Ruffini-like squared-mass formula for the four-dimensional Kerr-Newman-AdS super-entropic black hole, and then establish a set of very simple relations between thermodynamic quantities of the super-entropic Kerr-Newman-AdS${}_4$ black hole and its usual counterparts. Using these relations, the thermodynamic quantities of the Kerr-Newman-AdS${}_4$ super-entropic black hole can be obtained from those of the usual pro-type by taking the ultra-spinning limit properly. Then these relations are extended to the singly-rotating Kerr-AdS black holes in arbitrary dimensions and the double-rotating charged black hole in the five-dimensional minimal gauged supergravity. It can be inferred that the thermodynamic quantities of all super-entropic black holes obey similar limiting relations to those of their corresponding conventional rotating AdS black holes, and thus can be obtained by taking the ultra-spinning limit appropriately.

arXiv comment14 pages; to appear in PRD

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• Topological classes of thermodynamics of the four-dimensional static accelerating black holes
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• Are ultra-spinning Kerr-Sen-AdS${}_4$ black holes always super-entropic ?
• Thermodynamics and Null Geodesics of a Schwarzschild Black Hole Surrounded by a Dehnen Type Dark Matter Halo
• Thermodynamic topology of Phantom AdS Black Holes in Massive Gravity
• Topological classes of black holes in de-Sitter spacetime
• Aspects of the dyonic Kerr-Sen-AdS${}_4$ black hole and its ultraspinning version
• Universal thermodynamic topological classes of rotating black holes
• Topological classes of thermodynamics of the rotating charged AdS black holes in gauged supergravities
• Superentropic AdS Black Hole Shadows
• Consistent mass formulas for the four-dimensional dyonic NUT-charged spacetimes
• Light rings and shadows of static black holes in effective quantum gravity II: A new solution without Cauchy horizons
• Thermodynamic topological classes of the rotating, accelerating black holes
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• Superentropic Black Hole Shadows in Arbitrary Dimensions
• Null hypersurface caustics for high dimensional superentropic black holes
• Validity of Thermodynamic Laws and Weak Cosmic Censorship for AdS Black Holes and Black Holes in a Cavity
• Thermodynamic Instability of $3D$ Einstein-Born-Infeld AdS Black Holes
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• Super-entropic black holes in gravity's rainbow and determining constraints on rainbow functions
• Dimensional structure of thermodynamic topology in ultraspinning Kerr-AdS black holes
• Ultra-spinning Chow's black holes in six-dimensional gauged supergravity and their properties