Abstract
The separability of the massive Dirac equation in the non-extreme Kerr geometry in horizon-penetrating advanced Eddington-Finkelstein-type coordinates is shown. To this end, Kerr geometry is described by a Carter tetrad and the Dirac spinors and matrices are given in a chiral Newman-Penrose dyad representation. Applying Chandrasekhar's mode ansatz, the Dirac equation is separated into systems of ...
Abstract
The separability of the massive Dirac equation in the non-extreme Kerr geometry in horizon-penetrating advanced Eddington-Finkelstein-type coordinates is shown. To this end, Kerr geometry is described by a Carter tetrad and the Dirac spinors and matrices are given in a chiral Newman-Penrose dyad representation. Applying Chandrasekhar's mode ansatz, the Dirac equation is separated into systems of radial and angular ordinary differential equations. Asymptotic radial solutions at infinity, the event horizon, and the Cauchy horizon are explicitly derived. Their decay is analyzed by means of error estimates. Moreover, the eigenfunctions and eigenvalues of the angular system are discussed. Finally, as an application, the scattering of Dirac waves by the gravitational field of a Kerr black hole is studied. This work provides the basis for a Hamiltonian formulation of the massive Dirac equation in Kerr geometry in horizon-penetrating coordinates and for the construction of a functional analytic integral representation of the Dirac propagator.
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