Imprints of non-commutativity on charged black holes

Abstract

This work presents a comprehensive investigation of the gravitational phenomena that correspond to a non-commutative (NC) charged black hole, by incorporating NC geometry through a Moyal twist. We derive the deformed metric up to the second order of the NC parameter, utilizing the Seiberg-Witten map for the Reissner-Nordstrom black hole. We explore how non-commutativity modifies key thermodynamic properties, such as the Hawking temperature and heat capacity, and the existence of a remnant mass at the final stage of evaporation. Additionally, the study of Hawking radiation for bosonic and fermionic particles is discussed. Applying a perturbative method, scalar quasinormal modes are analyzed numerically. Furthermore, null geodesics and photon sphere stability are explored via curvature and topological methods. The shadow radius and deflection angle are computed to understand observational signatures. Lensing observables are compared to Event Horizon Telescope observations to provide probable constraints on the non-commutativity parameter. This study bridges theoretical predictions with astrophysical observations, offering insights into quantum gravity effects on black hole physics.

Figures (17)

• Figure 1: The Hawking temperature is plotted as a function of the event horizon radius $r_{h}$ for $Q=0.1$ and various values of $\Theta$.
• Figure 2: The Hawking temperature is plotted with respect to the mass $M$ for different values of $\Theta$, while the charge is set to $Q=0.1$.
• Figure 3: The heat capacity $C_{V}$ is shown as a function of the event horizon $r_{h}$ for different values of the charge $\Theta$, with the parameters set fixed at $Q=0.1$.
• Figure 4: The Hawking temperature and heat capacity are shown as a function of the event horizon $r_{h}$ for fixed values of the $Q = 0.1$ and $\Theta = 0.1$. The red and blue dashed lines correspond to the remnant and phase transition radius.
• Figure 5: The particle creation density $n^{ {(\Theta},{Q)}}$ is presented as a function of the frequency $\omega$ for a fixed value of $Q = 0.1$ and $M=1$ and different values of $\Theta$.