Annals of Mathematical Sciences and Applications
Volume 1 (2016)
Self-adjointness of the Dirac Hamiltonian for a class of non-uniformly elliptic boundary value problems
Pages: 301 – 320
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.
Dirac equation, Lorentzian manifold, essentially self-adjoint extension of the Dirac Hamiltonian, non-uniformly elliptic boundary value problem
2010 Mathematics Subject Classification
35F45, 35Q41, 81Q10