  We construct a four-dimensional spacetime using a three-dimensional contact
manifold equipped with a degenerate metric. The degenerate metric is set to be
compatible with the contact structure. The compatibility condition is defined
in this paper. Our construction yields a Ricci tensor of a particularly simple
form, which leads to a solution of the Einstein equation with a null dust and
cosmic strings. The solution includes two arbitrary functions: the energy
density of the null dust and the number density of the cosmic strings. When
there exist the cosmic strings, the spacetime is of Petrov type D. Otherwise,
the spacetime is conformally flat. For some simple matter densities, we examine
the Einstein equation in detail.
