Thermodynamics of two aligned Kerr-Newman black holes

Using the notion of thermodynamic length, the first law of thermodynamics is consistently derived for two binary configurations of equal Kerr-Newman black holes separated by a massless strut. As in the electrostatic systems of two Reissner-Nordstrom black holes and stationary vacuum systems of two Kerr black holes considered earlier, the thermodynamic length l turns out to be defined by the same simple formula l = L exp (gamma(0)), L being the coordinate length of the strut and gamma(0) the value of the metric function gamma on the strut, which permits the elaboration of l in a concise analytic form. The expression of the free energy in the case of two generic Kerr-Newman black holes is also proposed.