Black Hole Radiation Sparsity and Bekenstein Entropy Loss in Non-Commutative Schwarzschild Spacetime

Abstract: In this paper, we investigate the sparsity of black hole radiation, the Bekenstein entropy loss, and the total particle emission of a Schwarzschild black hole (SBH) within the framework of non-commutative (NC) gauge theory of gravity. First, we provide a brief review of black hole (BH) thermodynamics, computing both the deformed Hawking temperature and entropy. In this geometry, the divergent behavior of the temperature is removed, and a logarithmic correction to the entropy emerges. We then present the NC corrections to the Bekenstein entropy loss of the SBH alongside the total number of emitted particles. Our results show that the total number of emitted particles is proportional to the entropy behavior of the NC SBH, which is consistent with non-thermal radiation. Finally, we analyze the sparsity of Hawking radiation in this geometry, finding that the NC SBH exhibits extremely sparse radiation ($\hatη \gg 1$), which diverges at the final stage of evaporation as the black hole ceases to radiate.