The Initial Boundary Value Problem in General Relativity: The Umbilic Case

Abstract We give a short proof of local well-posedness for the initial boundary value problem in general relativity with sole condition requirement that is umbilic. This includes as special case totally geodesic we had previously addressed [ 8]. The based on wave coordinates and key observation momentum constraint always valid umbilic boundaries. allows greater freedom choice conditions, since imposing also provides Neumann conditions three four conditions. Moreover, condition, being geometric, implies geometric uniqueness sense Friedrich holds this specific case.