Abstract:
We show in detail that the Parikh-Wilczek tunneling method (PWTM), which was
designed for resolving the information loss problem in Hawking radiation (HR) fails whenever the
radiation occurs from an isothermal process. The PWTM aims to produce a non-thermal HR
which adumbrates the resolution of the problem of unitarity in quantum mechanics (QM), and
consequently the entropy (or information) conservation problem. The effectiveness of the method
has been satisfactorily tested on numerous black holes (BHs). However, it has been shown that the
isothermal HR, which results from the emission of the uncharged particles of the linear dilaton BH
(LDBH) described in the Einstein-Maxwell-Dilaton (EMD) theory, the PWTM has vulnerability in
having non-thermal radiation. In particular, we consider Painlev´e-Gullstrand coordinates (PGCs)
and isotropic coordinates (ICs) in order to prove the aforementioned failure in the PWTM. While
carrying out calculations in the ICs, we also highlight the effect of the refractive index on the null
geodesics.
