  We present the exact solution of Einstein's equation corresponding to a
static and plane symmetric distribution of matter with constant positive
density located below $z=0$. This solution depends essentially on two
constants: the density $\rho$ and a parameter $\kappa$. We show that this
space-time finishes down below at an inner singularity at finite depth. We
match this solution to the vacuum one and compute the external gravitational
field in terms of slab's parameters. Depending on the value of $\kappa$, these
slabs can be attractive, repulsive or neutral. In the first case, the
space-time also finishes up above at another singularity. In the other cases,
they turn out to be semi-infinite and asymptotically flat when $z\to\infty$.
  We also find solutions consisting of joining an attractive slab and a
repulsive one, and two neutral ones. We also discuss how to assemble a
"gravitational capacitor" by inserting a slice of vacuum between two such
slabs.
