Thermodynamics of rotating and non-rotating BTZ black holes through modified entropies

This study investigates the thermodynamic behaviour of two types of BTZ black holes: one is a rotating BTZ black hole and the other is a non-rotating charged BTZ black hole within the context of Sharma-Mittal and second-order exponential entropy. Important thermodynamic quantities, including the Gibbs free energy, derivatives of Gibbs free energy, heat capacity, sparsity and emission energy rate, are studied with respect to various parameters. It is found that the Sharma-Mittal entropy parameters and angular momentum strongly affect the stability and radiating nature of the rotating black hole. For charged black hole, phase transitions and stability are studied which lead to the conclusion that the AdS radius l and parameter R support sparsity, while the charge Q and entropy parameter δ suppress it. In contrast, the emission energy rate increases with Q and δ and decreases with increased values of l and R , suggesting the influence of geometrical and entropy parameters on black hole radiation dynamics. This study also considers the thermodynamic behaviour of a rotating BTZ black hole and a non-rotating charged BTZ black hole under the second-order exponential entropy. Thermodynamic quantities such as Gibbs free energy and heat capacity show phase transitions depending on the value of the AdS radius l , angular momentum J and electric charge Q . Higher entropy levels improve stability, with angular momentum and parameter l contributing in the opposite direction. The exponential corrections lower the sparsity and make the emission peaks sharper, meaning that the Hawking radiation is denser. Despite partial stabilization by larger Q and l , the charged black hole remains thermodynamically unstable, emphasizing the relevance of extended entropy formalisms in understanding black hole radiation and stability.

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