标题： 质量-角动量不等式对于多个黑洞 显示英文标题

标题： The Mass-Angular Momentum Inequality for Multiple Black Holes

摘要： 这是建立多黑洞猜想质量-角动量不等式的两篇论文中的第二篇，前提是极端黑洞的'无毛定理'成立。 更准确地说，证明了要么存在一个反例，即一个规则的轴对称静止真空时空，具有渐近平坦端和多个退化视界，并且是'ADM最小化'的，要么以下陈述成立。 对于具有多个端的爱因斯坦方程的完全、单连通、极大初始数据集，如果这些端是渐近平坦的或渐近圆柱形的，则在非负能量密度和轴对称性的假设下，其ADM质量有一个由总角动量平方根给出的下界。 此外，只有在极端Kerr时空的常时间截面上才能达到质量下界。 该证明基于一种具有双曲平面目标的奇异调和映射的新流，在这种流下，规范化的调和映射能量是单调非增的。 通过对方程及其线性化的解进行更精确的渐近分析，获得了该流的相关性质。 显示英文摘要

摘要： This is the second in a series of two papers to establish the conjectured mass-angular momentum inequality for multiple black holes, modulo the extreme black hole 'no hair theorem'. More precisely it is shown that either there is a counterexample to black hole uniqueness, in the form of a regular axisymmetric stationary vacuum spacetime with an asymptotically flat end and multiple degenerate horizons which is 'ADM minimizing', or the following statement holds. Complete, simply connected, maximal initial data sets for the Einstein equations with multiple ends that are either asymptotically flat or asymptotically cylindrical, admit an ADM mass lower bound given by the square root of total angular momentum, under the assumption of nonnegative energy density and axisymmetry. Moreover, equality is achieved in the mass lower bound only for a constant time slice of an extreme Kerr spacetime. The proof is based on a novel flow of singular harmonic maps with hyperbolic plane target, under which the renormalized harmonic map energy is monotonically nonincreasing. Relevant properties of the flow are achieved through a refined asymptotic analysis of solutions to the harmonic map equations and their linearization.