Universal Thermodynamic Topological Classes of BTZ Black Holes in Einstein and F(R) Gravity
This paper systematically demonstrates that the thermodynamic topological classification of three-dimensional BTZ black holes is fundamentally governed by the interplay of gravitational frameworks (Einstein vs. F(R)), matter field configurations, and ensemble choices, revealing how these factors collectively determine the black holes' intrinsic topological classes within a universal three-dimensional spacetime system.