Quantum Corrected Non-Thermal Radiation Spectrum from the Tunnelling Mechanism

Abstract

The 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 Galaxies 2015, 3 104 dynamical geometry during the emission of the particle and the quantum corrections to the semiclassical Hawking temperature.

Tunnelling Mechanism in Noncommutative Space with Generalized Uncertainty Principle and Bohr-Like Black Hole

“…Using the Hawking's periodicity argument [15,25,30,31,40] one obtains the modified GUP Schwarzschild like line element [25] ds…”

“…Further, by Hawking's periodicity argument [15,25,30,31] one easily obtains the modified GUP non-commutative effective Schwarzschild like line element as…”

Hawking-Like Radiation from the Trapping Horizon of Both Homogeneous and Inhomogeneous Spherically Symmetric Spacetime Model of the Universe

“…In semiclassical tunnelling analysis [5,6,[9][10][11][12][13]33], the radial null geodesic method is a common way of evaluating Hawking radiation. This method is simple as compared to the HJ method, but it has some limitations, namely:…”

“…Hartle and Hawking [4] subsequently derived the BH temperature at the semiclassical level using the Feynmann path integral. The mathematical complexity of the above procedures forces to develop semi-classical approaches [5][6][7][8][9][10][11] for studying BH radiation. However, these semi-classical techniques were classified into two approaches-the tunnelling approach of Parikh and Wilczek [5,6,[9][10][11][12][13][14][15][16] and the standard Hamilton-Jacobi (HJ) method (known as complex path integral formalism) by Padmanabhan et al [7,8].…”