# Tunnelling mechanism in non-commutative space with generalized uncertainty principle and Bohr-like black hole

## TL;DR

This paper explores how non-commutative geometry and the generalized uncertainty principle influence black hole radiation spectra, revealing modifications to the tunnelling mechanism and confirming the universality of Bekenstein's area quantization law.

## Contribution

It introduces GUP and non-commutative geometry corrections to black hole tunnelling radiation, extending the Bohr-like black hole model and analyzing entropy and area quantization.

## Key findings

- GUP and non-commutative geometry modify the black hole radiation spectrum.
- Bekenstein's area quantization law remains unaffected by these corrections.
- Black hole entropy retains dependence on quantum levels up to third order.

## Abstract

The paper deals with non-thermal radiation spectrum by tunnelling mechanism with correction due to the generalized uncertainty principle (GUP) in the background of non-commutative geometry. Considering the reformulation of the tunnelling mechanism by Banerjee and Majhi, the Hawking radiation spectrum is evaluated through the density matrix for the outgoing modes. The GUP corrected effective temperature and the corresponding GUP corrected effective metric in non-commutative geometry are determined using Hawking's periodicity arguments. Thus, we obtain further corrections to the non-strictly thermal black hole (BH) radiation spectrum which give new final distributions. Then, we show that the GUP and the non-commutative geometry modify the Bohr-like BH recently discussed in a series of papers in the literature. In particular, we find the intriguing result that the famous law of Bekenstein on the area quantization is affected neither by non-commutative geometry nor by the GUP. This is a clear indication of the universality of Bekenstein's result. In addition, we find that both the Bekentsein-Hawking entropy and the total BH entropy to third order approximation are still functions of the BH quantum level.