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