平衡4维和5维有符号质量的静态真空黑洞

M. Khuri, G. Weinstein, S. Yamada
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引用次数: 3

摘要

我们构造了一组新的4维和5维爱因斯坦方程的渐近平坦静态真空解,它可以解释为正质量黑洞和负质量黑洞的叠加。由此产生的时空在四维是轴对称的,在五维是双轴对称的,并且在远离负质量奇点的地方是规则的,例如沿轴不存在锥形奇点。在5维空间中,用于构造的符号质量黑洞的拓扑结构可以是球体$S^3$或环$S^1 \乘以S^2$;特别介绍了负质量静态黑环解。促进叠加的一个主要观察结果是,在Weyl-Papapetrou坐标系中,负质量奇点作为对特定类型格林函数的重叠奇异支持而出现。此外,对沿轴的圆锥奇点进行了仔细的分析,得到了它们在视界、负质量奇点和角上的传播公式。这些方法是鲁棒的,可以用来构造大量的进一步的例子。最后,我们证明了在4维中,任何两个有符号质量黑洞之间都不会发生平衡,而在5维中,两体平衡是可能的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Balancing Static Vacuum Black Holes with Signed Masses in 4 and 5 Dimensions
We construct a new set of asymptotically flat, static vacuum solutions to the Einstein equations in dimensions 4 and 5, which may be interpreted as a superposition of positive and negative mass black holes. The resulting spacetimes are axisymmetric in 4-dimensions and bi-axisymmetric in 5-dimensions, and are regular away from the negative mass singularities, for instance conical singularities are absent along the axes. In 5-dimensions, the topologies of signed mass black holes used in the construction may be either spheres $S^3$ or rings $S^1 \times S^2$; in particular, the negative mass static black ring solution is introduced. A primary observation that facilitates the superposition is the fact that, in Weyl-Papapetrou coordinates, negative mass singularities arise as overlapping singular support for a particular type of Green's function. Furthermore, a careful analysis of conical singularities along axes is performed, and formulas are obtained for their propagation across horizons, negative mass singularities, and corners. The methods are robust, and may be used to construct a multitude of further examples. Lastly, we show that balancing does not occur between any two signed mass black holes of the type studied here in 4 dimensions, while in 5 dimensions two-body balancing is possible.
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