  In general relativity, there is a well-developed formalism for working with
the approximation that a gravitational source is concentrated on a shell, or
codimension one surface. By contrast, there are obstacles to concentrating
sources on surfaces that have a higher codimension, for example, a string in a
spacetime with dimension greater than or equal to four. Here it is shown that,
by giving up some of the generality of the codimension one case, curvature can
be concentrated on submanifolds that have codimension two. A class of metrics
is identified such that (1) the scalar curvature and Ricci densities exist as
distributions with support on a co-dimension two submanifold, and (2) using the
Einstein equation, the distributional curvature corresponds to a concentrated
stress-energy with equation of state p equals minus the energy density, where p
is the isotropic pressure tangent to the submanifold. This is the appropriate
stress-energy to describe a self-gravitating brane that is governed by an area
action, or a brane world deSitter cosmology. The possibility of having a
different equation of state arise from a wider class of metrics is discussed.
