  We present two families of first-order in time and second-order in space
formulations of the Einstein equations (variants of the Arnowitt-Deser-Misner
formulation) that admit a complete set of characteristic variables and a
conserved energy that can be expressed in terms of the characteristic
variables. The associated constraint system is also symmetric hyperbolic in
this sense, and all characteristic speeds are physical. We propose a family of
constraint-preserving boundary conditions that is applicable if the boundary is
smooth with tangential shift. We conjecture that the resulting initial-boundary
value problem is well-posed.
