  We study transverse asymptotically flat spacetimes without horizons that
arise from brane matter sources. We assume that asymptotically there is a
spatial translation Killing vector that is tangent to the brane. Such
spacetimes are characterized by a tension, analogous to the ADM mass, which is
a gravitational charge associated with the asymptotic spatial translation
Killing vector. Using spinor techniques, we prove that the purely gravitational
contribution to the spacetime tension is positive definite.
