Why must the final state be stationary? I faced the following sentences:

We consider a gravitational collapse
  taking place in this spacetime. The singularity theorems assure us that a singularity will
  form. The assumption that the cosmic censorship conjecture is valid will then imply that
  the collapse must produce a black hole which will settle down to a stationary final state.

Can anyone explain to me why The assumption that the cosmic censorship conjecture is valid will then imply that
the collapse must produce a black hole which will settle down to a stationary final state?
Why must the final state be stationary?
 A: It is generally adopted that for a 'reasonable' class of 'regular' initial data the vacuum 
spacetime outside a collapsed object will settle down to a stationary Kerr black hole. This means that at late time the metric is just the regularly perturbed Kerr metric, and the 
perturbations decay. As was formulated by John Wheeler: 'Black holes have no hair'.
So for the final black hole state to be stationary it has to be stable and the perturbations must decay with time. This problem of stability is quite complex, and is not solved today.  The current strategy is to study, as a first step, linear wave equations on black hole backgrounds,
with the hope that sufficiently robust linear decay estimates can be bootstrapped
to produce a nonlinear stability proof.
See, for instance, the paper

Finster, F., Kamran, N., Smoller, J., & Yau, S. T. (2009). Linear waves in the Kerr geometry: A mathematical voyage to black hole physics. Bulletin of the American Mathematical Society, 46(4), 635-659, arXiv:0801.1428.

for the discussion of recent developments.
From the point of view of black hole thermodynamics the existence of stationary stable equilibrium configuration is the Zeroth law, with the constant surface gravity on the horizon playing the role of temperature.
