Abstract
The behavior of a charged massive Dirac field on a Reissner–Nordström–AdS black hole background is investigated. We first analyze the problem of the essential self-adjointness of the Dirac Hamiltonian, which is made difficult by the boundary-like behavior of spatial infinity, and we find that the Hamiltonian is essentially self-adjoint iff ; moreover, we determine the essential spectrum of the Hamiltonian. Then we focus on the analysis of the discharge problem for the case . We follow the Ruffini–Damour–Deruelle approach and, as in the standard Reissner–Nordström black hole case, we find that the existence of level-crossing between the positive and negative energy solutions of the Dirac equation is at the root of the pair-creation process associated with the discharge of the black hole.
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