Novel topological classes in black hole thermodynamics

TL;DR

This paper introduces new topological classes in black hole thermodynamics by analyzing black hole solutions as topological defects, revealing complex thermodynamic behaviors and evolution patterns that differ from previously known classifications.

Contribution

It identifies a novel topological class and two subclasses, expanding the framework of black hole thermodynamic classifications and highlighting their distinct properties.

Findings

Discovered a new topological class and subclasses in black hole thermodynamics.

Revealed unique thermodynamic behaviors of small and large black holes in these classes.

Demonstrated complex thermodynamic evolution in gauged supergravity black holes.

Abstract

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 $W^{0-\leftrightarrow 1+}$, $\overline{W}^{1+}$, and $\hat{W}^{1+}$, that extend beyond the four established categories proposed by Wei et al. [Phys. Rev. D 110, L081501 (2024)]. 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 behaviours, while the outermost large black hole states display a uniform pattern of stable behaviours. These classifications indicate thermodynamic properties in both the low and high Hawking temperature regimes that are strikingly different from the previously known four topological classes. In particular, we demonstrate that static charged AdS black holes in gauged supergravity exhibit an intricate thermodynamic evolution that is notably distinct from that of the Reissner-Nordstr\"om anti-de Sitter (RN-AdS) 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 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.