Quantum corrections and exotic criticality in charged rotating BTZ black holes

Abstract

We investigate quantum corrections to the thermodynamics of charged, rotating BTZ black holes in AdS spacetime using both Generalized Uncertainty Principle (GUP) and exponential entropy corrections. The Hamilton-Jacobi tunneling method yields the Hawking temperature and its GUP-modified form, revealing how Planck-scale effects suppress thermal radiation. Exponential corrections to the Bekenstein-Hawking entropy lead to modified expressions for internal energy, Helmholtz and Gibbs free energies, pressure, enthalpy, and heat capacity. The AdS radius 8 emerges as a critical parameter: smaller values enhance gravitational confinement and thermodynamic stability, while larger values weaken these effects. The heat capacity remains positive across parameter space, ruling out second-order phase transitions. However, the JT coefficient exhibits remarkable oscillatory behavior near rh approximate to 1.05, alternating between heating and cooling phases during isenthalpic expansion. These oscillations intensify with increasing 8, indicating reduced stability in weakly curved AdS backgrounds. Gravitational red-shift calculations in the weak-field limit show that the logarithmic charge coupling produces unbounded growth at large distances, with strong 8-dependence providing observational signatures. Our results demonstrate that (2+1)-dimensional black holes possess richer thermodynamic structure than their higher-dimensional counterparts, with quantum corrections introducing novel critical phenomena while preserving overall stability. These findings connect microscopic quantum gravity effects to macroscopic thermodynamic behavior, offering new perspectives on black hole physics in lower dimensions.