  We use AdS/CFT to construct the gravitational dual of a 5D CFT in the
background of a non-extremal rotating black hole. Our boundary conditions are
such that the vacuum state of the dual CFT corresponds to the Unruh state. We
extract the expectation value of the stress tensor of the dual CFT using
holographic renormalisation and show that it is stationary and regular on both
the future and the past event horizons. The energy density of the CFT is found
to be negative everywhere in our domain and we argue that this can be
understood as a vacuum polarisation effect. We construct the solutions by
numerically solving the elliptic Einstein--DeTurck equation for stationary
Lorentzian spacetimes with Killing horizons.
