An integrability theorem for harmonic maps of interest in General Relativity

Monday, December 10, 2012 -
3:15pm to 4:15pm
Einstein's Equations have been extensively studied in the context of integrability for several decades, drawing on results from inverse scattering to algebraic curves. In this talk, we will give a generalized notion of integrability for axially symmetric harmonic maps into symmetric spaces and prove that under some mild restrictions, all such maps are integrable. A primary application of the result involves generating $N$-soliton harmonic maps into the Grassmann manifold $SU(p,q) / S( U(p) x U(q) )$, a special case of which recovers the Kerr and Kerr-Newman family of solutions to the Einstein vacuum and Einstein-Maxwell equations, respectively. This is joint work with S. Tahvildar-Zadeh.
Speaker: 
Shabnam Beheshti
Rutgers University
Event Location: 
Fine Hall 314