# An integrability theorem for harmonic maps of interest in General Relativity

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Shabnam Beheshti, Rutgers University
Fine Hall 314

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.