  We present a general proof on the equivalence of the comoving-coordinate
approach, where the wall is fixed at a constant coordinate variable, and
moving-wall approach, where the wall is moving in a background static
space-time, in the domain wall space-times without reflection symmetry. We
further provide a general procedure to construct the comoving coordinates in
the domain wall space-times, where the two regions separated by an infinite
thin wall have different cosmological constant $\Lambda$ and Schwartzschild
mass $M$. By solving Israel's junction conditions in the thin-wall limit, the
gravitational fields of spherical, planar and hyperbolic domain wall
space-times with M=0 in the two different comoving coordinate systems are
obtained. We finally discuss the global structure of these domain wall
space-times.
