Universal thermodynamic topological classes of three-dimensional BTZ black holes

Abstract

We establish a universal thermodynamic topological classification for three-dimensional static neutral Bañados-Teitelboim-Zanelli (BTZ), charged BTZ, and rotating BTZ black holes. We demonstrate that in all three cases (static neutral BTZ, charged BTZ, and rotating BTZ black holes), both the innermost small black hole states and the outermost large black hole states exhibit stable thermodynamic behavior. In the low-temperature limit, all three cases exhibit a thermodynamically stable small black hole state. Conversely, in the high-temperature limit, each system admits a thermodynamically stable large black hole state. Through this analysis, we have rigorously shown that static neutral, charged, and rotating BTZ black holes are consistently classified within the $W^{1+}$ category. Our results demonstrate that neither the charge parameter nor the rotation parameter exerts significant influence on the universal thermodynamic topological classification of three-dimensional static neutral BTZ black holes. This reveals a fundamental dichotomy: while angular momentum and electric charge dominate the thermodynamic topology of four-dimensional static black holes, their effects become negligible in the three-dimensional static BTZ case, highlighting a dimension-driven divergence in black hole thermodynamic behavior.

6 pages, 6 figures, 4 tables, to appear in PLB

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Cited by in corpus (6)

• ${\tilde{W}}^{1+}$ subclass: Extending the topological classification of black hole thermodynamics
• Thermodynamics and topological classifications of static non-extremal four-charge AdS black hole in the five-dimensional $\mathcal{N}=2$, $STU-W^{2}U$ gauged supergravity
• Novel topological subclass in Hourava-Lifshitz black holes
• Topology of black hole thermodynamics: A brief review
• Thermodynamic Topology and Photon Spheres Analysis of Black Holes in Brane-World: Insights from Barrow Entropy
• Dimensional structure of thermodynamic topology in ultraspinning Kerr-AdS black holes