The study of axially symmetric stationary multi-black-hole configurations and the force between co-axially rotating black holes involves, as a first step, an analysis on the “boundary regularity” of the so-called reduced singular harmonic maps. We carry out this analysis by considering those harmonic maps as solutions to some homogeneous divergence systems of partial differential equations with singular coefficients. Our results extend previous works by Weinstein (Comm Pure Appl Math 43:903–948, 1990; Comm Pure Appl Math 45:1183–1203, 1992) and by Li and Tian (Manu Math 73(1):83–89, 1991; Commun Math Phys 149:1–30, 1992; Differential geometry: PDE on manifolds, vol 54, pp. 317–326, 1993). This paper is based on the Ph.D. thesis of the author (Singular harmonic maps into hyperbolic spaces and applications to general relativity, PhD thesis, The State University of New Jersey, Rutgers, 2009).
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机译：轴向对称固定多黑洞构型和同轴旋转黑洞之间的力的研究首先涉及分析所谓的简化奇异谐波图的“边界规则性”。我们通过将那些谐波映射作为具有奇异系数的偏微分方程的某些齐次发散系统的解来进行分析。我们的结果扩展了Weinstein（Comm Pure Appl Math 43：903–948，1990; Comm Pure Appl Math 45：1183–1203，1992）和Li and Tian（Manu Math 73（1）：83–89，1991）的先前著作。 ； Commun Math Phys 149：1–30，1992；微分几何：流形上的PDE，第54卷，第317–326页，1993）。本文基于博士学位。作者的论文（奇异谐波映射到双曲空间及其在广义相对论中的应用，博士学位论文，新泽西州立大学，罗格斯分校，2009年）。
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