Absence of an Effective Horizon for Black Holes in Gravity's Rainbow
  We argue that the divergence in time for the asymptotic observer occurs because of specifying the position of the Horizon beyond the Planck scale. In fact, a similar divergence in time will also occur for an in-going observer in Gravity's Rainbow, if we again specify the position of the Horizon beyond the Planck scale. On the other hand, if we accept the occurrence of a minimum measurable length scale associated with a universal invariant maximum energy scale in Gravity's Rainbow, then the time taken by both the in-going and asymptotic observers will be finite. 
Ahmed Farag Ali, Mir Faizal and Barun Majumder
gr-qc hep-th