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The separability of the massive Dirac equation in the non-extreme Kerrgeometry in horizon-penetrating advanced Eddington-Finkelstein-type coordinatesis shown. To this end, the Kerr geometry is described in the Newman-Penroseformalism by a regular Carter tetrad and the Dirac spinors and matrices aredefined in a chiral Newman-Penrose dyad representation. ApplyingChandrasekhar's mode ansatz, the Dirac equation is separated into radial andangular systems of ordinary differential equations. Asymptotic radial solutionsat infinity, the event horizon, and the Cauchy horizon are derived, and thedecay of the associated errors is analyzed. Moreover, specific aspects of theangular eigenfunctions and eigenvalues are discussed. Finally, as anapplication, the scattering of massive Dirac particles by the gravitationalfield of a rotating Kerr black hole is studied. This work provides the basisfor a Hamiltonian formulation of the massive Dirac equation in the non-extremeKerr geometry in horizon-penetrating coordinates and for the construction of anintegral spectral representation of the Dirac propagator that yields thedynamics of Dirac particles outside, across, and inside the event horizon, upto the Cauchy horizon.

The Massive Dirac Equation in the Kerr Geometry: Separability in Eddington-Finkelstein-type Coordinates and Asymptotics