Nonlinear electrodynamics effects on the geometry, thermodynamics, and quantum dynamics of (2+1)-dimensional black holes

Black holes in (2+1) dimensions serve as valuable toy models for understanding key aspects of real astrophysical black holes, providing insights into quantum gravity and thermodynamic properties. In this work, we present a novel (2+1)-dimensional black hole solution coupled with nonlinear electrodynamics (NLED). This extension of the well-known charged Bañados-Teitelboim-Zanelli (BTZ) black hole allows for a detailed investigation of the geometric and thermodynamic properties influenced by nonlinear electromagnetic fields. The introduction of the NLED parameter α modifies the black hole metric, leading to significant corrections in thermodynamic quantities such as the Hawking temperature and entropy. Using quantum tunneling methods, we derive the modified Hawking temperature, showing its explicit dependence on NLED corrections. Furthermore, we analyze entropy modifications that incorporate quantum statistical mechanics methods, revealing the impact of logarithmic corrections and the Generalized Uncertainty Principle (GUP). Additionally, we examine the propagation of a massive scalar field in this black hole background by solving the radial Klein-Gordon equation numerically. The NLED parameter introduces additional terms in the effective potential, affecting quantum field scattering, particle trapping, and the behavior of the photon sphere. We further study geodesic motion and highlight the influence of NLED on the deflection of light and the black hole shadow, suggesting potential observational signatures of these corrections. Finally, we investigate fundamental frequencies associated with quasi-periodic oscillations (QPOs) in the black hole accretion disk, offering a possible avenue for testing NLED effects through astrophysical observations. Therefore, this study offers insights into the observable signatures of NLED-modified black holes and their potential relevance in astrophysical and gravitational wave experiments.