Absence of an effective Horizon for black holes in Gravity's Rainbow

¹ Center for Fundamental Physics, Zewail City of Science and Technology - 12588, Giza, Egypt
² Department of Physics, Faculty of Science, Benha University - Benha, 13518, Egypt
³ Department of Physics and Astronomy, University of Waterloo - Waterloo, Ontario, N2L 3G1, Canada
⁴ Department of Physics, IIT Gandhinagar - Ahmedabad, India
⁵ Department of Physics, Montana State University - Bozeman, MT, USA

^(a) ahmed.ali@fsc.bu.edu.eg
afarag@zewailcity.edu.eg
^(b) f2mir@uwaterloo.ca
^(c) barunbasanta@iitgn.ac.in

Received: 12 September 2014
Accepted: 24 December 2014

Abstract

We argue that the divergence in time for an 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.