Novel topological classes in black hole thermodynamics

By viewing black hole solutions as topological defects in thermodynamic parameter space, we unveil a novel topological class and two new topological subclasses, respectively, denoted as W0−↔1+, W¯1+, and W¹+, that extend beyond the four established categories proposed by Wei. Within the newly identified class and these two novel subclasses, the innermost small black hole states exhibit a distinct sequence of unstable, stable, and stable behaviors, while the outermost large black hole states display a uniform pattern of stable behaviors. These classifications indicate thermodynamic properties both in the low and high Hawking temperature regimes that are strikingly different from the previously known four topological classes. In particular, we demonstrate that the static charged anti–de Sitter black holes in gauged supergravity exhibit an intricate thermodynamic evolution that is notably distinct from that of the Reissner-Nordström anti–de Sitter black hole. From a topological perspective, we emphasize the advantages and potential of investigating thermodynamic phase transitions in these black hole spacetimes, an area that has been rarely explored in the previous research. Our findings not only enrich and sharpen the framework of topological classifications in black hole thermodynamics but also represent a significant stride toward unraveling the fundamental nature of black holes and gravity.