Impact of Loop Quantum Gravity on the Topological Classification of Quantum-Corrected Black Holes

We investigated the thermodynamic topology of quantum-corrected AdS-Reissner-Nordström black holes in Kiselev spacetime using non-extensive entropy formulation derived from Loop Quantum Gravity (LQG). Through systematic analysis, we examined how the Tsallis parameter λ influences topological charge classification with respect to various equation of state parameters. Our findings revealed a consistent pattern of topological transitions: for λ=0.1, the system exhibited a single topological charge (ω=−1) with total charge W=−1, as λ increased to 0.8, the system transitioned to a configuration with two topological charges (ω=+1,−1) and total charge W=0. When λ=1, corresponding to the Bekenstein–Hawking entropy limit, the system displayed a single topological charge (ω=+1) with W=+1, signifying thermodynamic stability. The persistence of this pattern across different fluid compositions—from exotic negative pressure environments to radiation—demonstrates the universal nature of quantum gravitational effects on black hole topology.