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Self-Adjointness of the Dirac Hamiltonian for a Class of Non-Uniformly Elliptic Boundary Value Problems

We consider a boundary value problem for the Dirac equation in a smooth, asymptotically flat Lorentzian manifold admitting a Killing field which is timelike near and tangential to the boundary. A self-adjoint extension of the Dirac Hamiltonian is constructed. Our results also apply to the situation that the space-time includes horizons, where the Hamiltonian fails to be elliptic.

preprint2016arXivOpen access
Felix FinsterChristian Röken
math.APmath-phmath.MPgr-qc
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Felix FinsterChristian Röken

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