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arXiv 1711.06357gr-qchep-ph
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静止的黑洞有着纤细的毛发

Stationary black holes with stringy hair

Jens Boos, Valeri P. Frolov

摘要:

本文讨论了被宇宙弦特殊构型穿透的黑洞的性质。对于静态的黑洞,我们考虑在极限条件下的径向弦,当弦的数目增长到无穷大,而每根弦的张力趋于零时。在适当的极限下,弦分布的应力-能量张量是有限的。我们称这种物质为弦状物质。本文给出了带弦物质的带电静态黑洞的爱因斯坦方程的一个解,并讨论了有无宇宙学常数的情况。该解是两个度量的扭曲乘积。其中之一是变形的双球,其高斯曲率由弦物质的能量密度决定。我们讨论了相应的扭曲球到三维欧氏空间的嵌入,并制定了一致性条件。我们还发现了弦黑洞四维时空的Weyl张量不变量的平方与弦物质的能量密度之间的关系。本文的第二部分讨论了Kerr几何及其Kerr-NUT-(A)dS推广中的测试平稳弦。得到了在事件视界上正则的弦的显式解。利用这些解,计算了这些几何结构中弦物质的应力-能量张量。本文还讨论了利用这种弦从旋转黑洞中提取角动量的问题。

英文摘要:

We discuss properties of black holes which are pierced by special configurations of cosmic strings. For static black holes we consider radial strings in the limit when the number of strings grows to infinity while the tension of each single string tends to zero. In a properly taken limit the stress-energy tensor of the string distribution is finite. We call such matter stringy matter. We present a solution of the Einstein equations for an electrically charged static black hole with the stringy matter, with and without cosmological constant. This solution is a warped product of two metrics. One of them is a deformed two-sphere whose Gaussian curvature is determined by the energy-density of the stringy matter. We discuss the embedding of a corresponding distorted sphere into a three-dimensional Euclidean space and formulate consistency conditions. We also found a relation between the square of the Weyl tensor invariant of the four dimensional spacetime of the stringy black holes and the energy density of the stringy matter. In the second part of the paper, we discuss test stationary strings in the Kerr geometry and in its Kerr-NUT-(A)dS generalizations. Explicit solutions for strings that are regular at the event horizon are obtained. Using these solutions the stress-energy tensor of the stringy matter in these geometries is calculated. Extraction of the angular momentum from rotating black holes by such strings is also discussed.

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