Quantum tunneling from Schwarzschild black hole in non-commutative gauge theory of gravity

TL;DR

This paper investigates Hawking radiation as a tunneling process from a non-commutative Schwarzschild black hole within gauge theory of gravity, revealing thermal spectra, entropy corrections, and enhanced particle correlations due to non-commutativity.

Contribution

First study of Hawking radiation tunneling in non-commutative gauge theory of gravity, reconstructing NC Schwarzschild black hole and analyzing quantum emission spectra and entropy corrections.

Findings

Hawking temperature remains consistent across approaches

Deviations from pure thermal radiation at high frequencies

Logarithmic correction to black hole entropy

Abstract

In this letter, we present the first study of Hawking radiation as a tunneling process within the framework of non-commutative (NC) gauge theory of gravity. First, we reconstruct the non-commutative Schwarzschild black hole (NC SBH) within the gauge theory of gravity, employing the Seiberg-Witten (SW) map and the star product. Then, we compute the emission spectrum of outgoing massless particles using the quantum tunneling mechanism. In the first scenario, we calculate the tunneling rate of massless particles crossing the event horizon of the NC SBH with lower frequencies. Our results reveal pure thermal radiation. Notably, we find that the Hawking temperature remains consistent in both the classical thermodynamics and the quantum tunneling approach, suggesting equivalence between these two approaches in NC spacetime. However, in the case of massless particle emission with higher frequencies, we account for energy conservation resulting in the tunneling rate to deviate from pure thermal radiation. This tunneling rate remains consistent with an underlying unitary quantum theory. We establish a relationship between this deviation and the change in the black hole entropy, revealing a logarithmic correction to the entropy within this geometry. Furthermore, we demonstrate that non-commutativity enhances the correlations between two successively emitted particles. Additionally, we determine the NC density number of particle emission and conclude by discussing the implications of our findings.