  We begin a program of work aimed at examining the interior of a rotating
black hole with a non--zero cosmological constant. The generalisation of
Teukolsky's equation for the radial mode functions is presented. It is shown
that the energy fluxes of scalar, electromagnetic and gravity waves are regular
at the Cauchy horizon whenever the surface gravity there is less than the
surface gravity at the cosmological horizon. This condition is narrowly
allowed, even when the cosmological constant is very small, thus permitting an
observer to pass through the hole, viewing the naked singularity along the way.
