Domain wall space-times with a cosmological constant
  We solve vacuum Einstein's field equations with the cosmological constant in
space-times admitting 3-parameter group of isometries with 2-dimensional
space-like orbits. The general exact solutions, which are represented in the
advanced and retarded null coordinates, have two arbitrary functions due to the
freedom of choosing null coordinates. In the thin-wall approximation, the
Israel's junction conditions yield one constraint equation on these two
functions in spherical, planar, and hyperbolic domain wall space-times with
reflection symmetry. The remain freedom of choosing coordinates are completely
fixed by requiring that when surface energy density $\sigma_0$ of domain walls
vanishes, the metric solutions will return to some well-known solutions. It
leads us to find a planar domain wall solution, which is conformally flat, in
the de Sitter universe.
