New Insights into Harmonic Maps and Black Hole Physics
A recent paper titled "Asymptotic Analysis of Harmonic Maps With Prescribed Singularities" by Qing Han, Marcus Khuri, Gilbert Weinstein, and Jingang Xiong presents significant findings in the field of differential geometry and its implications for black hole physics. The authors focus on singular harmonic maps from three-dimensional Euclidean space to the hyperbolic plane, specifically those that maintain a bounded hyperbolic distance to extreme Kerr harmonic maps.
The study establishes that each harmonic map under consideration has a unique tangent harmonic map at the extreme black hole horizon. This tangent map is classified as shifted 'extreme Kerr' geodesics in the hyperbolic plane, influenced by two parameters: one related to angular momentum and the other to conical singularities. The authors also detail the rates of convergence to the tangent map and provide expansions for the asymptotically flat end.
These findings contribute to a complete regularity theory for harmonic maps from βR3 minus the z-axis to hyperbolic space with prescribed singularities. Furthermore, the analysis aids in proving the existence of the near horizon limit and calculating the associated near horizon geometries of extreme black holes. This work is positioned as the first in a series aimed at establishing the mass-angular momentum inequality for multiple black holes, which could have profound implications for our understanding of black hole dynamics and the nature of spacetime in extreme conditions.
The paper can be cited as: arXiv:2212.14826.