We study a stationary and axisymmetric binary system composed of two identical Kerr black holes, whose physical parameters satisfy the Smarr thermodynamic formula. Then, we use the formalism of geometrothermodynamics to show that the spatial distance between the black holes must be considered as a thermodynamic variable. We investigate the main thermodynamic properties of the system by using the contact structure of the phase-space, which generates the first law of thermodynamics and the equilibrium conditions. The phase transition structure of the system is investigated through the curvature singularities of the equilibrium space. It is shown that the thermodynamic and stability properties and the phase transition structure of the binary system strongly depend on the distance between the black holes.

中文翻译：

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黑洞二元系统的几何热力学

我们研究了一个由两个相同的克尔黑洞组成的静止轴对称二元系统，其物理参数满足斯马尔热力学公式。然后，我们用几何热力学的形式来证明黑洞之间的空间距离必须被视为一个热力学变量。我们利用相空间的接触结构研究了系统的主要热力学性质，产生了热力学第一定律和平衡条件。通过平衡空间的曲率奇点研究系统的相变结构。结果表明，二元系统的热力学和稳定性特性以及相变结构强烈依赖于黑洞之间的距离。