The Interior Volume of Kerr-AdS Black Holes

Abstract

The interior volume of black holes as defined by Christodoulou and Rovelli exhibits many surprising features. For example, it increases with time, even under Hawking evaporation. For some black holes, the interior volume is not even a monotonic increasing function of its area, which means one cannot infer how large a black hole is by just looking from the outside. Such a notion of volume, however, turns out to be useful in the context of holography, as it seems to be dual to the complexity of the boundary field theory. In this study, we investigate the properties of the interior volume of 4-dimensional Kerr-AdS black holes, fixing either the mass parameter $M$ or the physical mass $E$, whilst varying the values of the cosmological constant. We found that the volume as a function of the radial coordinate features a "double lobe" while fixing $M$, whereas fixing $E$ yields behaviors that are qualitatively similar to the asymptotically flat case. We briefly comment on the holographic complexity of Kerr-AdS black holes.

arXiv comment15 pages, 31 figures

References in corpus (31)

• Enthalpy and the Mechanics of AdS Black Holes
• Complexity Equals Action
• Black hole chemistry: thermodynamics with Lambda
• Complexity and Shock Wave Geometries
• Pressure and volume in the first law of black hole thermodynamics
• Complexity, action, and black holes
• The First Law of Thermodynamics for Kerr-Anti-de Sitter Black Holes
• Comments on Holographic Complexity
• On the Time Dependence of Holographic Complexity
• Holographic Complexity
• Complexity Growth for AdS Black Holes
• Subsystem Complexity and Holography
• How big is a black hole?
• Where is the PdV term in the first law of black hole thermodynamics?
• The Typical-State Paradox: Diagnosing Horizons with Complexity
• Holographic Complexity and Volume
• On the volume inside old black holes
• Black holes: Their large interiors
• The Persistence of the Large Volumes in Black Holes
• Holographic Thermalization from Kerr-AdS
• The Volume Inside a Black Hole
• The connection between holographic entanglement and complexity of purification
• Never Judge a Black Hole by Its Area
• Holographic Purification Complexity
• A Note on Physical Mass and the Thermodynamics of AdS-Kerr Black Holes
• Applied Holography of the AdS${}_5$-Kerr Spacetime
• Cosmic Censorship for AdS${}_5$-Kerr
• Kerr Black Holes Are Not Fragile
• Black hole horizons can hide positive heat capacity
• Kerr-AdS and Kerr-dS solutions revisited
• The volume of the black holes - the constant curvature slicing of the spherically symmetric spacetime

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• Maximal hypersurfaces and aspects of volume of the Kerr family of black holes