  We investigate the interior of regular axisymmetric and stationary black
holes surrounded by matter and find that for non-vanishing angular momentum of
the black hole the space time can always be extended regularly up to and
including an inner Cauchy horizon. We provide an explicit relation for the
regular metric at the inner Cauchy horizon in terms of that at the event
horizon. As a consequence, we obtain the universal equality $(8\pi J)^2 = A^+
A^-$ where $J$ is the black hole's angular momentum and $A^-$ and $A^+$ denote
the horizon areas of inner Cauchy and event horizon, respectively. We also find
that in the limit $J \to 0$ the inner Cauchy horizon becomes singular.
