  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.
