Optimal eigenvalue estimate for the Dirac-Witten operator on bounded domains with smooth boundary (Q1035769)

The Dirac-Witten operator, which can be thought as a generalization of the standard Dirac operator, has a main role in Witten's proof of the black hole versions of the positive energy-momentum theorem for asymptotically flat or asymptotically hyperbolic manifolds endowed with a symmetric 2-tensor of extrinsic curvature. The present paper gives dominant energy conditions for the Dirac-Witten operator on bounded domains, under four natural boundary conditions.