Annals of Mathematical Sciences and Applications

Volume 1 (2016)

Number 2

Self-adjointness of the Dirac Hamiltonian for a class of non-uniformly elliptic boundary value problems

Pages: 301 – 320

DOI: http://dx.doi.org/10.4310/AMSA.2016.v1.n2.a2

Authors

Felix Finster (Fakultät für Mathematik, Universität Regensburg, Germany)

Christian Röken (Fakultät für Mathematik, Universität Regensburg, Germany)

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.

Keywords

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

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