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Motivated by the cosmic censorship conjecture in mathematical relativity, weestablish the precise mass lower bound for an asymptotically flat Riemannian3-manifold with nonnegative scalar curvature and minimal surface boundary, interms of angular momentum and charge. In particular this result does notrequire the restrictive assumptions of simple connectivity and completeness,which are undesirable from both a mathematical and physical perspective.

The Positive Mass Theorem with Angular Momentum and Charge for Manifolds with Boundary