Scattering theory for Dirac fields near an extreme Kerr-de Sitter black hole

In this paper, we construct a scattering theory for classical mas-sive Dirac fields near the "double" horizon of an extreme Kerr-de Sitter blackhole. Our main tool is the existence of a conjugate operator in the sense of Mourre the-ory. Additionally, despite the fact that effects of the rotation are "amplified" near the double horizon, we show that one can still reduce our study to a 1-dimensional problem through an appropriate decomposition of the Hilbert space.