Volume dependent extension of Kerr-Newman black hole thermodynamics

Abstract

We show that the Hawking--Bekenstein entropy formula is modified by a factor of $8/3$ if one also considers a work term in the 1st law of thermodynamics by a pressure stemming from the Hawking radiation. We give an intuitive definition for the corresponding thermodynamical volume by the implicit definition $\epsilon =M{c}^2/V$, which is the average energy density of the Hawking radiation. This volume scales as $V\sim M^5$, agreeing with other suggestions. As a result the corresponding Smarr relation describes an extensive entropy and a stable effective equation of state $S(E,V)\sim E^{3/4}{V}^{1/4}$. These results pertain for charged and rotating Kerr-Newman black holes.

6 pages, 1 figure; accepted for publication in Phys. Lett. B

References in corpus (4)

• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• How big is a black hole?
• The volume of stationary black holes and the meaning of the surface gravity
• On the entropy associated with the interior of a black hole

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