The gravitational field of plane symmetric thick domain walls

Exact solutions of Einstein’s equations for a scalar field with a potential V(Φ) =V0 cos2(1−n) (Φ/f(n)) (0<n<1) are presented describing the gravitational field of thick, plane symmetric domain walls. The scalar field has a time-independent kinklike distribution, whereas the metric depends on a time coordinate. The metric is conformally flat and the hypersurfaces parallel to the wall (z=const) are three-dimensional de-Sitter spaces. A particle horizon exists on which the metric becomes Minkowski space. It is shown that the gravitational field experienced by a test particle is repulsive.