Quantum gravity effects on particle creation and evaporation in a non-commutative black hole via mass deformation

Abstract

In this work, we explore a gravitational non-commutative black hole by gauging the de Sitter SO(4,1) group and employing the Seiberg-Witten map. Specifically, we examine modifications of non-commutativity represented through mass deformation. Initially, we address modifications to Hawking radiation for bosonic particle modes by analyzing the Klein-Gordon equation in curved spacetimes. We compute the Bogoliubov coefficients, showing how $\Theta$ introduces a correction to the amplitude associated with particle creation. Additionally, we derive the power spectrum and the Hawking temperature within this framework. We also derive Hawking radiation from a tunneling perspective, leading to expressions for the power spectrum and particle number density. A similar analysis is performed for fermion particles. Remarkably, we obtain an analytical expression for black hole evaporation lifetime and compare our results with recent estimates of non-commutativity in the literature.