Thermodynamics of two aligned Kerr black holes

We investigate the first law of thermodynamics in the stationary axisymmetric configurations composed of two Kerr black holes separated by a massless strut. Our analysis employs the recent results obtained for the extended double-Kerr solution and for thermodynamics of the static single and binary black holes. We show that, similar to the electrostatic case, in the stationary binary systems the thermodynamic length ℓ is defined by the formula ℓ = L exp (γ0), where L is the coordinate length of the strut, and γ0 is the value of the metric function γ on the strut.