Thermodynamic phase structure and topological charge of Hayward-AdS black holes under phase space constraints

TL;DR

The paper investigates how a constraint that regularizes a singular black hole affects its thermodynamics in AdS space, comparing the singular solution to the Hayward-AdS regular black hole within an extended phase space where $P=-\Lambda/(8\pi)$. It derives the singular BH from Einstein gravity with nonlinear electrodynamics, then imposes a constraint $M=\frac{16 \times 2^{3/4}\pi Q^{3/2}}{\alpha^{1/4}}$ to obtain the Hayward-AdS BH, and analyzes $P$-$V$ and $T$-$r_+$ relations along with the Gibbs free energy. Thermodynamic topology via the $\phi$-mapping method is employed to classify the global phase-space structure, revealing a topological charge change from $W=-1$ for the singular BH to $W=+1$ for the Hayward-AdS BH. The singular case exhibits a rich phase structure with reentrant transitions, while the Hayward-AdS case retains $P$-$V$ criticality but with a distinct $G$-$T$ topology (an $8$-shaped to $0$-like to $C$-shaped evolution) and no RN-AdS-like swallowtail for $P<P_c$. Overall, the constraint not only regularizes geometry but also qualitatively reshapes the thermodynamic configuration space, with implications for stability and microstructure studies.

Abstract

We investigate the thermodynamic behavior of the Hayward-AdS black hole and compare it with its singular counterpart from which it can be constructed through the imposition of an additional constraint. The singular black hole displays a rich phase structure, including reentrant phase transitions reminiscent of those observed in higher-dimensional Kerr-AdS spacetimes. After the constraint is imposed, the resulting Hayward-AdS black hole continues to exhibit Van der Waals-type $P-V$ criticality. However, its Gibbs free energy profile differs qualitatively from that of standard RN-AdS black holes. In addition, we extend the analysis by employing thermodynamic topology to characterize the global structure of the phase space. We find that the topological charge of the singular black hole is $-1$, whereas that of the Hayward-AdS black hole becomes $+1$. This change of topological charge indicates that the constraint not only regularizes the geometry but also induces a qualitative transformation in the thermodynamic configuration space.

Figures (8)

• Figure 1: The $P-r_{+}$ and the $T-r_{+}$ curves of the singular black hole for fixed $Q=0.01$ and $\alpha=2$.
• Figure 2: The behaviors of $C-r_{+}$ for different values of $P$ for fixed $Q=0.01$ and $\alpha=2$. Here $P_0=0.3$.
• Figure 3: The $G-T$ curves for different values of $P$ for fixed $Q=0.1$ and $\alpha=2$. Here $~P_z=0.018$, and $P_0=0.016$.
• Figure 4: The $T-r_{+}$ and $P-r_{+}$ curves of the Hayward-AdS black hole with fixed $\alpha=1.5$.
• Figure 5: The behaviors of $C-r_{+}$ for the Hayward-AdS black holes for fixed $\alpha=1.5$.