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arXiv 1306.1019gr-qc
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旋转黑洞的形状

On the shape of rotating black-holes

Martin Reiris, Maria Eugenia Gabach Clement

摘要:

我们给出了一个彻底的描述形状的旋转轴对称稳定黑洞(表观)视界适用于动态或静态制度。它被发现,旋转表现在扩大其中心区域(旋转增厚),限制其整体形状的范围内,一个给定的面积A和角动量J(非零)的稳定孔形成一个precompact家庭(旋转稳定),并强制其整个几何形状接近极端克尔视界几何在几乎最大的旋转速度(强制成形)。结果,这是基于稳定性不等式,只取决于A和J。特别是,他们是完全独立的周围的几何形状的时空和存在的物质满足强能量条件。给出了子午线长度L与最大轴对称圆长度R之间的一组完整的关系式。我们还提供了具体的估计之间的距离的几何视界和极端克尔,仅在A和J.除了它自己的利益,工作有应用的箍猜想制定的Gibbons的Birkhoff不变量,贝肯斯坦-霍德熵界和研究的紧凑性类的固定黑洞时空。

英文摘要:

We give a thorough description of the shape of rotating axisymmetric stable black-hole (apparent) horizons applicable in dynamical or stationary regimes. It is found that rotation manifests in the widening of their central regions (rotational thickening), limits their global shapes to the extent that stable holes of a given area A and angular momentum J (non zero) form a precompact family (rotational stabilization) and enforces their whole geometry to be close to the extreme-Kerr horizon geometry at almost maximal rotational speed (enforced shaping). The results, which are based on the stability inequality, depend only on A and J. In particular they are entirely independent of the surrounding geometry of the space-time and of the presence of matter satisfying the strong energy condition. A complete set of relations between A, J, the length L of the meridians and the length R of the greatest axisymmetric circle, is given. We also provide concrete estimations for the distance between the geometry of horizons and that of the extreme Kerr, in terms only of A and J. Besides it own interest, the work has applications to the Hoop conjecture as formulated by Gibbons in terms of the Birkhoff invariant, to the Bekenstein-Hod entropy bounds and to study the compactness of classes of stationary black-hole space-times.

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