to understand why this highly nontrivial inequality should hold unless censorship can be thought of as providing the underlying physical reason behind it.

The inequalities (\[eq:pen\]), (\[eq:mj\]) and (\[eq:JA\]) can be divided into two groups:

1.  $\sqrt{\frac{A}{16\pi}}\leq m$: the area appears as lower bound.

2.  $\sqrt{|J|} \leq m$ and $ 8\pi |J| \leq A $: the angular momentum appears as lower bound and the area appears as upper bound.

The mathematical methods used to study these two groups are, up to now, very different. This review is mainly concerned with the second group.

Finally, we mention that for the Kerr black hole there exists a remarkable equality of the form $(8\pi J)^2 =A^+A^-$, where $A^+$ and $A^-$ denote the areas of event and Cauchy horizon (see figure \[fig:kerr-diag\]). This equality has been proved for general stationary spacetimes in the following series of articles [@Ansorg:2009yi] [@Hennig:2009aa] [@Ansorg:2008bv]. It has recently received considerable attention in the string community (see [@Cvetic:2010mn] and [@Visser:2012wu] and references therein). The key property used in these studies is that the product of horizon areas is independent of the mass of the black hole. It is interesting to note that there exists, up to now, no generalization of 