The Dirac propagator in the Kerr-Newman metric

We give an alternative proof of the completeness of the Chandrasekhar ansatz for the Dirac equation in the Kerr-Newman metric. Based on this, we derive an integral representation for smooth compactly supported functions which in turn we use to derive an integral representation for the propagator of solutions of the Cauchy problem with initial data in the above class of functions. As a by-product, we also obtain the propagator for the Dirac equation in the Minkowski space-time in oblate spheroidal coordinates.Comment: 29 pages, modifications in the abstract and in the introduction, small improvements in section 2.

The generalized Heun equation in QFT in curved space-times

In this article we give a brief outline of the applications of the generalized Heun equation (GHE) in the context of Quantum Field Theory in curved space-times. In particular, we relate the separated radial part of a massive Dirac equation in the Kerr-Newman metric and the static perturbations for the non-extremal Reissner-Nordstr\"{o}m solution to a GHE.Comment: 7 pages, some small improvements in section

Heun equation, Teukolsky equation, and type-D metrics

Starting with the whole class of type-D vacuum backgrounds with cosmological constant we show that the separated Teukolsky equation for zero rest-mass fields with spin $s=\pm 2$ (gravitational waves), $s=\pm 1$ (electromagnetic waves) and $s=\pm 1/2$ (neutrinos) is an Heun equation in disguise.Comment: 27 pages, corrected typo in eq. (1

Quantum Effects for the Dirac Field in Reissner-Nordstrom-AdS Black Hole Background

The behavior of a charged massive Dirac field on a Reissner-Nordstrom-AdS black hole background is investigated. The essential self-adjointness of the Dirac Hamiltonian is studied. Then, an analysis of the discharge problem is carried out in analogy with the standard Reissner-Nordstrom black hole case.Comment: 18 pages, 5 figures, Iop styl