标题： 关于旋转黑洞的形状 显示英文标题

标题： On the shape of rotating black-holes

摘要： 我们给出了适用于动态或静态情况的旋转轴对称稳定黑洞（视界）形状的详细描述。发现旋转体现在其中央区域的扩展（旋转增厚），将其整体形状限制到一定程度，使得给定面积A和角动量J（非零）的稳定黑洞形成一个预紧族（旋转稳定化），并强制其整个几何结构在接近最大旋转速度时接近极端Kerr视界几何（强制成型）。这些结果基于稳定性不等式，仅依赖于A和J。特别是它们完全独立于时空的周围几何结构以及满足强能量条件的物质的存在。给出了A、J、子午线长度L和最大轴对称圆长度R之间的一组完整关系。我们还提供了仅以A和J为基准的视界几何与极端Kerr几何之间距离的具体估计。除了其自身的兴趣外，这项工作在Gibbons用Birkhoff不变量表述的Hoop猜想、Bekenstein-Hod熵界限以及研究静态黑洞时空类的紧凑性方面有应用。 显示英文摘要

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.