(i) and (ii) constitute the standard picture of the gravitational collapse. Relevant examples where this picture is confirmed (and where the role of angular momentum is analyzed) are the collapse of neutron stars studied numerically in [@Baiotti:2004wn] [@Giacomazzo:2011cv].

The black hole uniqueness theorem implies that the final stationary state postulated in (ii) is given by the Kerr black hole. Let us denote by $m_0,
J_0, A_0$, respectively, the mass, angular momentum and horizon area of the remainder Kerr black hole. Penrose argument runs as follows. Take a Cauchy surface $S$ in the spacetime such that the collapse has already occurred. This is shown in figure \[fig:5\].

![The Penrose diagram of a gravitational collapse. The initial Cauchy surface is denoted by $S$. The area $A$ increase along the event horizon. The mass $m$ decrease along null infinity. We have assumed axial symmetry and hence the angular momentum remains constant along null infinity $J=J_0$.[]{data-label="fig:5"}](penrose-ineq-js-p.pdf){width="50.00000%"}

Let ${\Sigma}$ denotes the intersection of the event horizon with the Cauchy surface $S$ and let $A$ be its area. Let $(m, J)$ be the total mass and angular momentum at spacelike infinity. These quantities can be computed from the initial surface $S$. By the black hole area 