We investigate a previously constructed stationary solution of the vacuum Einstein equations, which represents a system of two non-extreme black holes with equal masses and opposite NUT charges, connected by a Misner string with tension. For large separations, the inverse square law force measured by this tension is attractive or repulsive, according to the relative values of the masses and NUT charges. For small separations, the force is always repulsive, so that the system cannot collapse to a single black hole. For given values of the black hole masses and NUT charges, there is a unique configuration such that the Misner string is tensionless. This behaves asymptotically as the Kerr solution, but can be overspinning while remaining free from a ring singularity, thus evading the usual black hole uniqueness theorems. All double black hole and string configurations satisfy a generalized first law of black hole mechanics where the two black holes and the Misner string are treated on an equal footing.

我们研究了真空爱因斯坦方程的先前构造的平稳解，该爱因斯坦方程表示具有相等质量和相反NUT电荷的两个非极端黑洞的系统，这些黑洞由具有张力的Misner弦连接。对于较大的间距，根据质量和NUT电荷的相对值，由该张力测量的平方反比力具有吸引力或排斥力。对于小间距，该力始终是排斥力，因此系统不会崩溃到单个黑洞。对于黑洞质量和NUT电荷的给定值，存在一种独特的配置，使得Misner线无张力。它的行为与Kerr解的渐近性一样，但在保持环奇异性的同时可能过度旋转，从而避免了通常的黑洞唯一性定理。