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Thermodynamic Topology of 4D Charged AdS Black Holes with $F^{αβ}F^{γλ}R_{αγβλ}$ Coupling

Mehdi Sadeghi, Faramarz Rahmani

Abstract

We investigate the thermodynamic phase transitions of a four-dimensional charged anti-de Sitter black hole endowed with a non-minimal coupling of the form $F^{αβ}F^{γλ}R_{αγβλ}$. Using perturbative methods, we derive a consistent black hole solution and analyze its thermodynamics through both conventional equilibrium techniques and a topological defect classification approach. The system displays van der Waals-like critical behavior, with a swallow-tail structure in the free energy and distinct phase branches. The topological analysis independently confirms the existence of critical points and classifies the system within the universal topological scheme for black hole thermodynamics.

Thermodynamic Topology of 4D Charged AdS Black Holes with $F^{αβ}F^{γλ}R_{αγβλ}$ Coupling

Abstract

We investigate the thermodynamic phase transitions of a four-dimensional charged anti-de Sitter black hole endowed with a non-minimal coupling of the form . Using perturbative methods, we derive a consistent black hole solution and analyze its thermodynamics through both conventional equilibrium techniques and a topological defect classification approach. The system displays van der Waals-like critical behavior, with a swallow-tail structure in the free energy and distinct phase branches. The topological analysis independently confirms the existence of critical points and classifies the system within the universal topological scheme for black hole thermodynamics.
Paper Structure (6 sections, 71 equations, 5 figures, 2 tables)

This paper contains 6 sections, 71 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. $F^{\alpha\beta}F^{\gamma\lambda}R_{\alpha\gamma\beta\lambda}$-Coupled AdS Black Hole and Perturbative Solutions
  3. Conventional Thermodynamic Analysis
  4. Topological Formalism for Phase Transitions
  5. Topological Phase Structure with $F^{\alpha\beta}F^{\gamma\lambda}R_{\alpha\gamma\beta\lambda}$ Coupling
  6. Conclusions

Figures (5)

  • Figure 1: Van der Waals-like behavior in the $P$–$r_h$ and $T$–$r_h$ diagrams. (a) Pressure as a function of $r_h$ at the critical temperature $T_c = 0.17$ for several charge values. (b) Temperature as a function of $r_h$ at the critical pressure $P_c = 0.05$ for several charge values.
  • Figure 2: Local and global thermodynamic behavior of the system. (a) Heat capacity for subcritical pressure, revealing stable/unstable/stable phase structure. (b) Helmholtz free energy displaying the swallow-tail shape characteristic of van der Waals-like phase transitions.
  • Figure 3: Topological structure and phase diagram for the black hole system.
  • Figure 4: Contour mapping and deflection angle analysis. (a) The curves show the evolution of the $\phi$-field components in the $\phi$-plane as the contours $C_i$ in the $(r_h, \Theta)$ plane are traversed. The three zero points in the original coordinate space map to the origin $(0,0)$ in this representation, with the direction of each curve indicating the sign of the corresponding winding number. (b) The evolution of the deflection angle $\Omega(\vartheta)$ around each zero point provides independent confirmation of the winding numbers.
  • Figure 5: Unit vector field topology and deflection angle analysis. (a) The unit vector field and its boundary behavior for $Q = 0.8$, $P = 0.01 < P_c = 0.02$, and $\tau = 12$ demonstrate that the system belongs to Case III of the topological classification. (b) The evolution of the deflection angle $\Omega(\vartheta)$ around each zero point independently verifies the winding numbers $(+1, -1, +1)$ associated with the three black hole states.