Scattering of Dirac Fields in the Interior of Kerr-Newman(-Anti)-de Sitter Black Holes via Comparison and Symmetry Operators

Abstract

In this paper we construct a scattering theory for the massive and charged Dirac fields in the interiors of sub-extremal Kerr-Newman(-anti)-de Sitter black holes. More precisely, we show existence, uniqueness and asymptotic completeness of scattering data for such Dirac fields from the event horizon of the black hole to the Cauchy horizon. Our approach relies on constructing the wave operators where the Hamiltonian of the full dynamics is time-dependent. To prove asymptotic completeness, we use two methods. The first involves a comparison operator, while for the second we introduce and employ a symmetry operator of the Dirac equation.