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

TL;DR

This paper investigates how non-commutative geometry, modeled through mass deformation, influences Hawking radiation and black hole evaporation, providing analytical results and comparing with existing non-commutative models.

Contribution

It introduces a novel approach to non-commutative black holes using mass deformation and analyzes particle creation and evaporation effects analytically.

Findings

Mass deformation modifies Hawking radiation amplitude.

Derived analytical expression for black hole lifetime.

Compared results with existing non-commutative models.

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.