Analysis of Hawking evaporation, shadows, and thermodynamic geometry of black holes within the Einstein SU(N) non-linear sigma model

Abstract

We explore the intriguing properties of black holes in the Einstein SU(N) non-linear sigma model with a focus on stability, thermodynamic geometry, the Hawking evaporation process, and shadow characteristics. Our study utilizes a novel generalized entropy framework which unify several established entropy models including Bekenstein, Barrow, Tsallis-Cirto, and Tsallis-Zamora entropies. By deriving expressions for specific heat capacity and Gibbs free energy, we unveil distinct stability regions and phase transitions. A key highlight of our investigation is the interplay between the flavor number and AdS length, which we show to profoundly influence black hole evaporation time via the Stefan-Boltzmann law. Numerical simulations reveal that higher flavor numbers shorten evaporation times and reduce the black hole's shadow radius, shedding light on the impact of SU(N) symmetry. Additionally, we employ Weinhold, Ruppeiner, and Quevedo thermodynamic geometries to compute scalar curvatures, visualizing microscopic interactions among black hole molecules. This comprehensive analysis bridges thermodynamic stability, quantum evaporation, and optical signatures, offering fresh perspectives on the rich dynamics of black holes in the Einstein SU(N) non-linear sigma model.