Singular harmonic maps into hyperbolic spaces and applications to general relativity

Harmonic maps with singular boundary behavior from a Euclidean domain into hyperbolic spaces arise naturally in the study of axially symmetric and stationary spacetimes in general relativity. In particular, the study of multi-black-hole configurations and the force between co-axially rotating black holes requires, as a first step, an analysis on the boundary regularity of the "next order term" of those 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. We then apply our result to study the regularity of axially symmetric and stationary electrovac spacetimes, which extends previous works by Weinstein and by Li and Tian. This dissertation is based on a preprint of the author.Ph.D.Includes bibliographical references (p. 51-52)by Luc L. Nguye