Introduces a holographic pressure and volume for static spherically symmetric black holes via quasi-local thermodynamics, showing large black holes become extensive in the large-system limit while small ones do not.
The Volume of Black Holes
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abstract
We propose a definition of volume for stationary spacetimes. The proposed volume is independent of the choice of stationary time-slicing, and applies even though the Killing vector may not be globally timelike. Moreover, it is constant in time, as well as simple: the volume of a spherical black hole in four dimensions turns out to be just ${4 \over 3} \pi r_+^3$. We then consider whether it is possible to construct spacetimes that have finite horizon area but infinite volume, by sending the radius to infinity while making discrete identifications to preserve the horizon area. We show that, in three or four dimensions, no such solutions exist that are not inconsistent in some way. We discuss the implications for the interpretation of the Bekenstein-Hawking entropy.
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Treating the cosmological constant as pressure in black hole thermodynamics yields an extended dictionary with enthalpy, thermodynamic volume, and chemical-like phase transitions including Van der Waals behavior, reentrant transitions, and triple points.
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Holographic pressure and volume for black holes
Introduces a holographic pressure and volume for static spherically symmetric black holes via quasi-local thermodynamics, showing large black holes become extensive in the large-system limit while small ones do not.
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Black hole chemistry: thermodynamics with Lambda
Treating the cosmological constant as pressure in black hole thermodynamics yields an extended dictionary with enthalpy, thermodynamic volume, and chemical-like phase transitions including Van der Waals behavior, reentrant transitions, and triple points.