Seminar

In this talk we consider the conformal formulation of the Einstein constraint equations on a compact manifold M with boundary dM.

Under certain assumptions on the data, we show that near- and far-from-constant mean curvature solutions to the conformal formulation exist when a class of Robin boundary conditions commonly used in the literature for modeling black holes are imposed on dM.

This work is a natural extension of the work done recently by Holst and Tsogtgerel (2013), Holst, Nagy, and Tsogtgerel (2008), Maxwell (2004, 2005), and Dain (2004). Dain and Maxwell addressed initial data engineering for space-times that evolve to contain black holes, determining solutions to the conformal formulation on an asymptotically Euclidean manifold in the constant mean curvature (CMC) setting, with interior boundary conditions representing excised interior black hole regions.