Domain wall space-times with a cosmological constant

Chih-Hung Wang, Hing-Tong Cho, Yu-Huei Wu
2011 Physical Review D  
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
more » ... domain wall space-times with reflection symmetry. The remain freedom of choosing coordinates are completely fixed by requiring that when surface energy density σ_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.
doi:10.1103/physrevd.83.084014 fatcat:c3y3tusozretdalj6q7ykrahdm