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

Abstract

We investigated the thermodynamic topology of quantum-corrected AdS-Reissner-Nordstr & ouml;m 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 lambda influences topological charge classification with respect to various equation of state parameters. Our findings revealed a consistent pattern of topological transitions: for lambda=0.1, the system exhibited a single topological charge (omega=-1) with total charge W=-1, as lambda increased to 0.8, the system transitioned to a configuration with two topological charges (omega=+1,-1) and total charge W=0. When lambda=1, corresponding to the Bekenstein-Hawking entropy limit, the system displayed a single topological charge (omega=+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.