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-Nordström black holes and stationary vacuum systems of two Kerr black holes considered earlier, the thermodynamic length $\ell$ turns out to be defined by the same simple formula $\ell =L\exp ({\gamma }_0)$, $L$ 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 $\ell$ in a concise analytic form. The expression of the free energy in the case of two generic Kerr-Newman black holes is also proposed.

Figure 1

Location of two equal counterrotating KN black holes with the same charges on the symmetry axis.

Figure 2

Location of two equal counterrotating KN black holes with opposite charges on the symmetry axis.