https://doi.org/10.1140/epjp/s13360-025-06844-6
Regular Article
Gibbs–Duhem equation for Kerr–Newman black holes
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Cd. Universitaria, 04510, Ciudad de Mexico, Mexico
a
osmar.lopez@correo.nucleares.unam.mx
b
josue.mateos@correo.nucleares.unam.mx
c
socolovs@nucleares.unam.mx
Received:
1
September
2025
Accepted:
9
September
2025
Published online:
20
September
2025
We show that the intensive variables associated with the outer and inner horizons of the Kerr–Newman black hole: absolute temperatures, angular velocities and electromagnetic potentials, obey a Gibbs–Duhem type relation, which is closely related, but however distinct, to the Smarr equation. Thus, analogously as in ordinary thermodynamics, 
, 
and 
are not independent quantities. The relation also holds in the Kerr and Reissner–Nordström cases, while in the Schwarzschild case it is trivially fulfilled due to the zeroth law of black hole mechanics.
© The Author(s) 2025
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