Repulsive and attractive planar walls in general relativity

The method of a previous paper is generalized to yield all solutions to Einstein's equations for planar-symmetric walls composed of surface energy density $\sigma$ and tension $\tau$, with constant ratios in the physical range $\frac{\tau }{\sigma }\le 1$. Special cases include domain walls, walls of cosmic strings, dust walls, and (when $\tau <0\mathrm{}$) pressure walls. Attention is focused on the sense in which a wall is gravitationally repulsive when the tension is strong, the sense in which repulsion gives way to attraction as $\frac{\tau }{\sigma }$ is reduced below the value ½, and the way in which these features are reflected in the motion of the wall. Also studied is the way in which the unique static planar-symmetric solution fits within the classes of solutions.