  We derive new lower bounds for the first eigenvalue of the Dirac operator of
an oriented hypersurface $\Sigma$ bounding a noncompact domain in a spin
asymptotically flat manifold (M n , g) with nonnegative scalar curvature. These
bounds involve the boundary capacity potential and, in some cases, the capacity
of $\Sigma$ in (M n , g) yielding several new geometric inequalities. The proof
of our main result relies on an estimate for the first eigenvalue of the Dirac
operator of boundaries of compact Riemannian spin manifolds endowed with a
singular metric which may have independent interest.
