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

First boundary Dirac eigenvalue and boundary capacity potential