Thermodynamic geometry and interacting microstructures of BTZ black holes

In this work, we present a study to probe the nature of interactions between black hole microstructures for the case of the Banados, Teitelboim, and Zanelli (BTZ) black holes. Even though BTZ black holes without any angular momentum or electric charge thermodynamically behave as an ideal gas, i.e., with noninteracting microstructures; in the presence of electric charge or angular momentum, BTZ black holes are associated with repulsive interactions among the microstructures. We extend the study to the case of exotic BTZ black holes with mass $M=\ensuremath{\alpha}m+\ensuremath{\gamma}\frac{j}{l}$ and angular momentum $J=\ensuremath{\alpha}j+\ensuremath{\gamma}lm$, for arbitrary values of $(\ensuremath{\alpha},\ensuremath{\gamma})$ ranging from purely exotic $(\ensuremath{\alpha}=0,\ensuremath{\gamma}=1)$ to slightly exotic $(\ensuremath{\alpha}>\frac{1}{2},\ensuremath{\gamma}<\frac{1}{2})$ to highly exotic $(\ensuremath{\alpha}<\frac{1}{2},\ensuremath{\gamma}>\frac{1}{2})$. We find that, unlike the normal BTZ black holes [the case ($\ensuremath{\alpha}=1$, $\ensuremath{\gamma}=0$)], there exist both attraction as well as repulsion dominated regions in all the cases of exotic BTZ black holes.

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