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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 , which is the average energy density of the Hawking radiation.
This volume scales as , agreeing with other suggestions. As a result the corresponding Smarr relation describes an extensive entropy and a stable effective equation of state . These results pertain for charged and rotating Kerr-Newman black holes._x000D_
T.S. Biró, V. G. Czinner, H. Iguchi, P. Ván, Volume dependent extension of Kerr-Newman black hole thermodynamics, Physics Letters B 803(10) (2020) 135344