Compressibility of rotating black holes
arXiv:1109.0198 · doi:10.1103/PhysRevD.84.127503
Abstract
Interpreting the cosmological constant as a pressure, whose thermodynamically conjugate variable is a volume, modifies the first law of black hole thermodynamics. Properties of the resulting thermodynamic volume are investigated: the compressibility and the speed of sound of the black hole are derived in the case of non-positive cosmological constant. The adiabatic compressibility vanishes for a non-rotating black hole and is maximal in the extremal case --- comparable with, but still less than, that of a cold neutron star. A speed of sound is associated with the adiabatic compressibility, which is is equal to for a non-rotating black hole and decreases as the angular momentum is increased. An extremal black hole has when the cosmological constant vanishes, and more generally is bounded below by .
8 pages, 1 figure, uses revtex4, references added in v2
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