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

Abstract

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.

14 pages, LaTeX, 1 figure, minor improvements (published version)

Cited by in corpus (8)

• Interior-Boundary Conditions for Many-Body Dirac Operators and Codimension-1 Boundaries
• Local Dirac energy decay in the 5D Myers-Perry geometry using an integral spectral representation for the Dirac propagator
• The Fermionic Entanglement Entropy of the Vacuum State of a Schwarzschild Black Hole Horizon
• Baryogenesis in Minkowski Spacetime
• A Positive Quasilocal Mass for Causal Variational Principles
• Lectures on Linear Stability of Rotating Black Holes
• An Integral Representation for the Dirac Propagator in the Reissner-Nordström Geometry in Eddington-Finkelstein Coordinates
• The Dirac equation across the horizons of the 5D Myers-Perry geometry : Separation of variables, radial asymptotic behaviour and Hamiltonian formalism