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We begin a program of work aimed at examining the interior of a rotatingblack hole with a non--zero cosmological constant. The generalisation ofTeukolsky's equation for the radial mode functions is presented. It is shownthat the energy fluxes of scalar, electromagnetic and gravity waves are regularat the Cauchy horizon whenever the surface gravity there is less than thesurface gravity at the cosmological horizon. This condition is narrowlyallowed, even when the cosmological constant is very small, thus permitting anobserver to pass through the hole, viewing the naked singularity along the way.Comment: 21 pages, NCL93-TP10 (TeX

Stability of the Cauchy horizon in Kerr--de Sitter spacetimes