An exact and analytical solution of four dimensional vacuum General Relativity representing a system of two static black holes at equilibrium is presented. The metric is completely regular outside the event horizons, both from curvature and conical singularities. The balance between the two Schwarzschild sources is granted by an external gravitational field, without the need of extra matter fields besides gravity, nor strings or struts. The geometry of the solution is analysed. The Smarr law, the first and the second law of black hole thermodynamics are discussed.

中文翻译：

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处于平衡状态的双黑洞系统

提出了代表两个处于平衡状态的静态黑洞系统的四维真空广义相对论的精确解析解。该度量在事件视界之外是完全规则的，无论是曲率还是圆锥奇点。两个史瓦西源之间的平衡是通过外部引力场实现的，除了引力之外，不需要额外的物质场，也不需要弦或支柱。分析解决方案的几何形状。讨论了斯马尔定律、黑洞热力学第一和第二定律。