Generalized Lematre time for rotating and charged black holes and its near-horizon properties

We consider the behavior of the analogue of the Lemaître time when a particle approaches the horizon of a rotating black hole. For the Kerr metric, the aforementioned time coincides with the Doran or Natario time but we consider a more general class of metrics. We scrutiny relationship between (i) its .niteness or divergence, (ii) the forward-in-time condition, (iii) the sign of a generalized momentum/energy, (iv) the validity of the principle of kinematic censorship. The latter notion means impossibility to release in any event an energy which is literally in.nite. As a consequence, we obtain a new explanation, why collisions of two particles inside the horizon do not lead to in.nite energy in their center of mass frame. The same results are also obtained for the Reissner-Nordström metric.