Harmonic Maps and applications to higher dimensional black holes
General Relativity, Geometry and Analysis: beyond the first 100 years after Einstein
27 November 16:00 - 17:00
Gilbert Weinstein - Ariel University
The problem of stationary $(n-3)$-axisymmetric stationary solutions of the Einstein vacuum equations in $n$-dimensional gravity reduces to a harmonic map from $\R^3$ into the symmetric space $SL(n-2,\R)/SO(n-2)$ with prescribed singularities along a subset of the $z$-axis. The singularities are prescribed using the so-called rod-structure, an $(n-3)$-tuple of relatively prime integers. These can be used to prescribe the topology of the horizon. In this talk, I will discuss a PDE method to prove existence and uniqueness of solutions to the reduced equations for every admissible configuration. If time allows, I will discuss the topology of the domain of outer communication of these solutions.
Please note: The venue for this seminar is the old seminar room in the main building of the institute.
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
KTH Royal Institute of Technology
Philippe G. LeFloch
University of California, Irvine