Quantum corrected non-thermal radiation spectrum from the tunnelling mechanism

TL;DR

This paper develops a quantum corrected model of black hole radiation spectrum using the tunnelling mechanism, incorporating dynamical geometry and quantum effects to refine the non-thermal emission spectrum.

Contribution

It introduces a quantum corrected effective temperature and metric, extending previous tunnelling models to include quantum and dynamical geometry corrections in black hole radiation.

Findings

Derived a quantum corrected non-thermal radiation spectrum.

Incorporated dynamical geometry effects into the tunnelling framework.

Provided a more accurate description of black hole emission spectra.

Abstract

Tunnelling mechanism is today considered a popular and widely used method in describing Hawking radiation. However, in relation to black hole (BH) emission, this mechanism is mostly used to obtain the Hawking temperature by comparing the probability of emission of an outgoing particle with the Boltzmann factor. On the other hand, Banerjee and Majhi reformulated the tunnelling framework deriving a black body spectrum through the density matrix for the outgoing modes for both the Bose-Einstein distribution and the Fermi-Dirac distribution. In contrast, Parikh and Wilczek introduced a correction term performing an exact calculation of the action for a tunnelling spherically symmetric particle and, as a result, the probability of emission of an outgoing particle corresponds to a non-strictly thermal radiation spectrum. Recently, one of us (C. Corda) introduced a BH effective state and was able to obtain a non-strictly black body spectrum from the tunnelling mechanism corresponding to the probability of emission of an outgoing particle found by Parikh and Wilczek. The present work introduces the quantum corrected effective temperature and the corresponding quantum corrected effective metric is written using Hawking's periodicity arguments. Thus, we obtain further corrections to the non-strictly thermal BH radiation spectrum as the final distributions take into account both the BH dynamical geometry during the emission of the particle and the quantum corrections to the semiclassical Hawking temperature.