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We investigate the interior of regular axisymmetric and stationary blackholes surrounded by matter and find that for non-vanishing angular momentum ofthe black hole the space time can always be extended regularly up to andincluding an inner Cauchy horizon. We provide an explicit relation for theregular metric at the inner Cauchy horizon in terms of that at the eventhorizon. 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 $A^+$ denotethe horizon areas of inner Cauchy and event horizon, respectively. We also findthat in the limit $J \to 0$ the inner Cauchy horizon becomes singular.

The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter